Born in Santa Ana, California, Stieb played varsity baseball at Southern Illinois University as an outfielder. Scouted by Bobby Mattick and Al LaMacchia of the Blue Jays as an outfield prospect in a varsity game, Stieb's performance failed to impress until he was pressed into service as a relief pitcher. His pitching surprised and convinced the Blue Jays to draft him.
He played for the Blue Jays from 1979 to 1992 and again in 1998. On September 2, 1990, he pitched the first (and, to date, only) no-hitter in Blue Jays history, defeating the Cleveland Indians 3–0. Previously, on September 24 and 30, 1988, Stieb had no-hitters broken up with two outs and two strikes in the top of the ninth inning in two consecutive home starts. He also took a no-hitter into the ninth inning in a 1985 game; this bid was broken up by back-to-back home runs and Stieb being replaced in the game before he recorded an out in the ninth. On August 4, 1989, he had a perfect game broken up with two outs in the ninth. It was the third time in two seasons that Stieb had lost a no-hitter with two out in the ninth inning. After an excellent 1990 season, a series of shoulder and back injuries early in the 1991 season ended his effective pitching years, culminating in a 4–6 season in 1992 that resulted in his release. Despite this, he was awarded a World Series ring, after the Blue Jays won their first championship later that year. In 1993, he played four games with the Chicago White Sox, before finally retiring due to lingering back problems. In 1998, after a five-year hiatus from baseball, Stieb returned to the Blue Jays and pitched in 19 games. He recorded one win and two saves, and started three games.
In 1985, Stieb signed with the Blue Jays what was then one of the richest contracts in baseball. The contract, including options exercisable by the team, was for a term of ten years and specified a salary that increased to $1.9 million in 1993, $2 million in 1994, and $2.1 million in 1995. While this was seen to be generous at the time the contract was signed, by the time the later years of the contract came around this was a bargain, considering that several players were receiving several times the amount per year. The Blue Jays voluntarily renegotiated the last three years of his contract to pay him a higher amount in recognition of his years of service.
During his career, Stieb won 176 games while losing 137. Only Jack Morris won more games in the 1980s. Stieb holds career records for Toronto pitchers in wins, games started, shutouts, strikeouts, complete games and a variety of other categories. Stieb appeared in seven All-Star games, also a Blue Jays team record.
On August 29, 2010, Stieb threw the ceremonial first pitch at the Rogers Centre, celebrating the 20th anniversary of his no-hitter game, with the anniversary coming four days after the celebration. Stieb's number 37 was engraved on the pitcher's mound for the game.
Stieb entered the league primarily as a power pitcher, relying on a high, inside fastball to strike batters out. The brushback pitch was an integral part of his repertoire to back batters off the plate, and was especially tough on right-handed hitters in this respect. As a result, he led the league in hit batsmen a few years. But arguably his best pitch was his slider that had a late and very sharp break, especially difficult for right-handed batters to handle.
Later on in his career he developed his breaking ball repertoire, and he became very effective with a "dead fish" curveball that would break into the dirt as the batter swung.
Stieb had a high-strung personality and was known as a fierce competitor on the mound; he was regularly seen having animated conversations with himself during pitches when in difficult situations. Whereas with other pitchers this would be seen as a sign of weakness, with Stieb it was perceived as the best way to motivate himself to get out of a jam. Early in his career, Stieb would also frequently yell at his teammates after errors, or plays that he thought they should have made. In later years, Stieb mellowed somewhat, although a fierce glare after a botched play was still not uncommon.
Stieb is still involved with the Blue Jays spring training camps and currently resides in Reno, Nevada.
Stieb's autobiography was titled Tomorrow I'll Be Perfect, and was released in 1986.