Pizarro was born in Santurce, Puerto Rico. He began his baseball career in 1955 in Puerto Rico as a pitcher for the Cangrejeros de Santurce. During the 1957–1958 Winter League of Puerto Rico of the Liga de Béisbol Profesional de Puerto Rico (Puerto Rico Baseball League), he played for the Criollos de Caguas and was selected as the Most Valuable Player of the season. From 1959 to 1960 he pitched for the last time in Puerto Rico for the Cangrejeros del Santurce.
Pizarro signed with the Milwaukee Braves as an amateur free agent in 1956. After going 27–6 with a 2.06 earned run average in the minors, he made his major league debut on May 4, 1957 against the Pittsburgh Pirates at only twenty years old. He pitched seven strong innings, giving up only one run, however, the Braves managed only two hits off opposing pitcher Vern Law, and Pizzarro lost his debut, 1–0. For the season, he went 5–6 with a 4.62 ERA. The Braves beat the New York Yankees in a seven-game World Series that year; Pizarro's only appearance came in Milwaukee's 12–3 loss in game three.
He split 1958 between Milwaukee and the triple A Wichita Braves, and was again included on the Braves' post-season roster as they faced the Yankees in the World Series for the second year in a row. This time the Yankees won the Series in seven games. Pizarro's only appearance again came in a loss in game five.
Pizarro remained with the Braves through 1960, compiling a 23–19 record and 3.93 ERA in Milwaukee. On December 15, 1960, he was traded with Joey Jay to the Cincinnati Reds for Roy McMillan, then immediately sent by the Reds with Cal McLish to the Chicago White Sox for Gene Freese.
Pizarro enjoyed his greatest success as a member of the Chicago White Sox. In 1961, despite being the youngest pitcher in the starting rotation, Pizarro emerged as the staff's ace, leading the Chisox with fourteen wins, 188 strikeouts and 194.2 innings pitched. He also made fourteen appearances out of the bullpen, and earned his first career save on August 27. He was given the opening day nod in 1962, and pitched a complete game 2–1 victory over the Los Angeles Angels. In 1963, he was named to the American League All-Star roster, and pitched a scoreless seventh inning during the All-Star Game.
Pizarro's best season was 1964, when he went 19–9 with a 2.56 ERA and four shutouts. Coincidentally, it was also his best season with the bat, as he batted .211 with a career high three home runs and career high fifteen runs batted in.
From there, things rapidly deteriorated for him. Injuries limited Pizarro to just eighteen starts in 1965. In 1966, he was used primarily in relief. Despite a respectable 8–6 record and 3.76 ERA in 34 appearances, he pitched only 88.2 innings. Following the season, he was purchased by the Pittsburgh Pirates.
Though he made nine starts for the 1967 Pirates, he was mainly a relief pitcher, earning a career high nine saves. He was limited to "mop up duty" by manager Larry Shepard in 1968. He appeared in twelve games with the Pirates prior to being placed on waivers; eleven were losses. The one win, Pizarro entered the game with the Pirates trailing, and earned the win himself.
The Boston Red Sox claimed Pizarro off waivers on June 27. He was used primarily as a starter in Boston, going 6–6 with six complete games as a starter. He also earned two saves for the Bosox. At the start of the 1969 season, he, Dick Ellsworth and Ken Harrelson were sent to the Cleveland Indians for Joe Azcue, Vicente Romo and Sonny Siebert. Toward the end of the season, he was placed on waivers and claimed by the Oakland Athletics.
After beginning the 1970 season with Oakland's triple A affiliate, Pizarro was released and signed a minor league contract with the California Angels. He was 9–0 for the Hawaii Islanders when the Angels dealt him to the Chicago Cubs for Archie Reynolds.
On September 11, he shut out the St. Louis Cardinals at Wrigley Field. In his next start, he shutout Tom Seaver and the New York Mets 1–0 at Shea Stadium. The one run was a solo shot by Pizarro in the eighth inning. Seaver had won seven in a row at that point. His previous loss came on August 1, also courtesy of a complete game by Pizarro. It would be more than 40 years before another starting pitcher broke a 0–0 tie by hitting a home run in the eighth inning or later: Clayton Kershaw of the Dodgers did this, also in the eighth inning, on Opening Day 2013.
For the 1971 season, Pizarro went 7–6 with a 3.46 ERA. He was 4–5 with a 3.94 ERA in 1972. He spent most of the first half of the 1973 season assigned to the Cubs' triple A affiliate, the Wichita Aeros. After a blown save against the Atlanta Braves on June 17, Pizarro was placed on waivers. He was claimed by the Houston Astros on July 8.
Pizarro was 2–2 with a 6.56 ERA out of Houston's bullpen in 1973. He was released the following Spring, and rejoined the Pittsburgh Pirates. The Pirates won the National League East by a game and a half over the St. Louis Cardinals, allowing Pizarro to return to the post season for the first time since 1958. His only appearance in the 1974 National League Championship Series came in the fourth game, which the Los Angeles Dodgers won to head to the 1974 World Series.
Pizarro was inducted into the Hall of Fame of the Caribbean Confederation and the Puerto Rican Sports Hall of Fame.American League All-Star (1963, 64)
American League Leader in strikeouts per 9 innings pitched (1961, 62)
AmerIcan League Leader in fielding average as pitcher (1963, 64)
National League pennant team (1957, 58)
World Series champion team (1957)
Pizarro had a .202 lifetime batting average with 8 home runs and 66 RBIs.