Righetti was born in San Jose, California. His father, Leo, was a professional baseball player. His brother, Steve, is thirteen months older than Dave. Leo trained his sons to become baseball players. Dave and Steve starred for their Lincoln Glen Little League team, Letterman, with Dave playing in the outfield and Steve playing shortstop.
Righetti attended Pioneer High School. Paddy Cottrell, a scout for the Texas Rangers of Major League Baseball, noticed Righetti and suggested he become a pitcher due to his throwing motion. As a senior, he was named to the All-League team. Righetti enrolled in San Jose City College, where he continued his development as a pitcher on the school's baseball team. He was named the junior college player of the year, beating out teammate Dave Stieb.
At Cottrell's urging, the Rangers selected Righetti on January 11, 1977, in the first round (10th overall pick) of the amateur draft. The Rangers selected Steve in the sixth round, and told Dave that they would only sign Steve if he signed. Both Righetti brothers signed with the Rangers. Dave made his professional debut that year in minor league baseball with the Asheville Tourists of the Class A Western Carolinas League, where he pitched to an 11–3 win–loss record.
In 1978, Righetti pitched for the Tulsa Drillers of the Class AA Texas League. In a July game against the Midland Rockhounds, Righetti recorded a league-record 21 strikeouts. Jerry Walker, a scout for the New York Yankees, was present in the stands. Yankees owner George Steinbrenner, while negotiating a trade with Rangers owner Brad Corbett that offseason, specifically waited until late in their negotiations to ask that Righetti be added to the trade. On November 10, 1978, the Yankees acquired Righetti, along with Juan Beniquez, Mike Griffin, Greg Jemison, and Paul Mirabella, while the Rangers acquired Sparky Lyle, Domingo Ramos, Mike Heath, Larry McCall, Dave Rajsich, and cash. The Yankees introduced Righetti as "the next Ron Guidry". Righetti was almost traded to the Minnesota Twins in January 1979; the Twins and Yankees were unable to complete a deal in which Righetti, Chris Chambliss, Juan Beniquez, and Damaso Garcia would have moved to Minnesota in exchange for Rod Carew.
Righetti made his major league debut with the Yankees on September 16, 1979, wearing uniform number 56. In this game against the Detroit Tigers he pitched five innings, striking out three and allowing three hits, six walks, and three earned runs. After Righetti made his second start, Yankees' manager Billy Martin declared that Righetti "will win 20 games next season". However, Righetti struggled with his control, and spent the 1980 season with the Columbus Clippers of the Class AAA International League, where he had a 6–10 win-loss record and a 4.63 ERA with 101 walks and 139 strikeouts in 142 innings.
Though Righetti pitched well in spring training in 1981, the Yankees did not have room for him on their roster, so he began the season with Columbus. After he pitched to a 5–0 record and 1.00 ERA with 50 strikeouts in 45 innings, the Yankees recalled Righetti from Columbus in May 1981. He was assigned uniform number 19. The Yankees reserved numbers ending in 9 for pitchers they viewed as having promise: Dick Tidrow wore 19 for the Yankees, while Catfish Hunter wore 29, Ron Davis wore 39, and Guidry wore 49. Righetti pitched strongly as a starter for the Yankees, posting an 8–4 win-loss record in 15 games started, with a 2.06 earned run average (ERA) and 89 strikeouts in 105 innings pitched during the 1981 season. Righetti won the American League's Rookie of the Year award, beating Rich Gedman and Bob Ojeda. Righetti defeated the Milwaukee Brewers twice during the 1981 American League Division Series. The Yankees reached the World Series that year; however, he was knocked out of game three of the 1981 World Series early, which was won by the Los Angeles Dodgers.
In 1982, Righetti pitched to an 8.53 ERA during spring training. Steinbrenner sought to demote Righetti to the minor leagues, but stated he "got outvoted then". Through June 1982, Righetti had pitched to a 5–5 win-loss record with a 4.23 ERA. Though his 77 strikeouts were fourth-best in the American League, his 62 walks were considered a problem. The Yankees demoted Righetti to the minor leagues, for what Steinbrenner termed a "2 1⁄2-week intensive brushing up". Sammy Ellis, Righetti's pitching coach with Columbus, said that Righetti had been rushing his pitching motion, which was likely due to anxiety. Working with Ellis, Righetti made four starts for the Clippers, recording 33 strikeouts in 26 innings, before he was recalled to New York. Righetti finished the 1982 season with 11 wins in 27 starts, with a 3.79 ERA and 162 strikeouts and 108 walks. His strikeouts were third-best in the AL, while his walks led the league.
On July 4, 1983, Righetti threw a no-hitter against the Boston Red Sox at Yankee Stadium. It was the first Yankee no-hitter since Don Larsen's perfect game in the 1956 World Series, and the first by a Yankee left-hander since 1917. It was also the first time ever a no-hitter occurred during a Yankees-Red Sox rivalry game. Righetti recorded a swinging strikeout against Wade Boggs to end the game. Twenty-five years later, Righetti reminisced about the game:
"My biggest worry, because I had a tendency to fall toward third base, was him (Boggs) tapping a ball between me and Mattingly and me trying to get to first base...I threw a lot of fastballs during the at bat, but the last slider I ended up throwing, he happened to miss it. Thank goodness."
In 1984, Righetti was moved to the Yankees' bullpen due to an excess of starters, and replaced Goose Gossage as the team's closer. Despite the excess of starters, many criticized the move, arguing that Righetti was more valuable pitching as a starter, where he would accrue more innings.
Entering his first game as a relief pitcher with the bases loaded, Righetti did not allow an inherited runner to score, retiring the final seven batters of the game. He proved even more effective in relief, averaging 32 saves per season over the next seven years with the Yankees, and being named an All-Star in 1986 and 1987. On October 4, 1986, he saved both games of a doubleheader against the Boston Red Sox, finishing the season with 46 saves, and breaking the major league record shared by Dan Quisenberry and Bruce Sutter. The record would stand until Bobby Thigpen saved 57 games for the Chicago White Sox in 1990. Righetti retained the single-season record for left-handers until 1993, when Randy Myers saved 53 games for the Chicago Cubs; Righetti still owns the AL record for left-handers.
Righetti became a free agent after the 1987 season. Amid rumors that Righetti would sign a three-year contract worth $20 million with the Tokyo Giants of Nippon Professional Baseball, Righetti's agent acknowledged that the Giants did make Righetti an offer, but stated that the value was considerably less than what was reported, and stated that Righetti would continue to pitch in MLB. The contract offer was later estimated at $10 million. Righetti chose to re-sign with the Yankees, signing a three-year contract worth $4.5 million.
Righetti struggled with the Yankees early in the 1988 season, blowing four consecutive save opportunities, resulting in boos from the Yankee Stadium crowds. He then recorded five saves in consecutive opportunities.
Righetti became concerned with the direction the Yankees were taking, as they had traded away Rickey Henderson, Jack Clark, and Dave Winfield. After the 1990 season, Righetti signed as a free agent with the San Francisco Giants, receiving a four-year contract worth $10 million. While with the Giants in 1991, he broke Lyle's major league record for left-handers of 238 career saves; Righetti's record would stand until 1994, when John Franco surpassed his eventual total of 252. Righetti saved only 24 games in 1991, and the following two years saw him ineffective in middle relief roles; his career as a closer was over. Righetti made a start on June 10, 1992, his first start since September 1983.
Released by the Giants after the 1993 season, he crossed the Bay to sign as a free agent with the Oakland Athletics. After beginning 1994 with the Athletics, he was released, and signed as a free agent with the Toronto Blue Jays in May 1994, playing for the Jays wearing number 24. Righetti had a 0–1 win-loss record and 6.75 ERA for the Blue Jays.
After that season he was released by the Blue Jays, and in spring 1995 he signed as a free agent with the Chicago White Sox, wearing number 45 with the team. On November 9, 1995, he was again granted free agency; but no team signed him, and Righetti retired to end his 16-year career, finishing with 252 saves, a 3.46 ERA, and a record of 82–79 in 718 games.
Since 2000, Righetti has been the pitching coach for the Giants. Despite uncertainty if he would return to the Giants for the 2007 season due to a managerial change, Righetti announced in early November 2007 that he would remain with the Giants in his present role. He was the pitching coach for the pitching staff that included Matt Cain, Madison Bumgarner, Tim Lincecum, Jonathan Sanchez, and Brian Wilson that won the 2010, 2012, and 2014 World Series. An analysis by Fangraphs showed that Righetti has an uncanny knack for teaching pitchers to not give up home runs.
He and his wife had triplets (two daughters and one son), who were born in 1991; Righetti's wife's sister served as a surrogate mother.