Pitching for the Brooklyn/Los Angeles Dodgers, he teamed with Sandy Koufax during the late 1950s and 1960s to form one of the most dominating pitching duos in history. The ferocious hurler (nicknamed "Big D" by fans) used brushback pitches and a sidearm fastball to intimidate batters, and his 154 hit batsmen remain a modern National League record.

In 1962, Drysdale won 25 games and the Cy Young Award, and set a record with 58 consecutive scoreless innings in 1968; the record was ultimately broken by fellow Dodger Orel Hershiser 20 years later. In 1963, he struck out 251 batters and even won a World Series Game (Game 3 at Los Angeles' Dodger Stadium).In 1965, the all-around athlete was the Dodgers' only .300 hitter and tied his own National League record for pitchers with seven home runs. That year he won 23 games and led the Dodgers to only their 3rd world championship in Los Angeles, he ended his career by winning 209 games, striking out 2,486 batters, pitched in 167 complete games and had 49 shutouts. He was later inducted into the Baseball Hall of Fame in 1984, and had his number 53 officially retired at Dodger Stadium on 1 July 1984.

Don Drysdale retired after the 1969 season and became a broadcaster for not just the Dodgers (from 1988 up until his death in 1993), but also the Montréal Expos (1970-1971), Texas Rangers (1972), California Angels (1973-1979), Chicago White Sox (1982-1987), and ABC (1978-1986).

While at ABC Sports, Drysdale not only did baseball telecasts, but also Superstars and Wide World of Sports. In 1979, Drysdale covered the World Series Trophy presentation ceremonies for ABC. In 1984, Drysdale did play-by-play (alongside fellow Hall of Famers Reggie Jackson and Earl Weaver) for the thrilling National League Championship Series between the San Diego Padres and Chicago Cubs.

On October 6, 1984 at San Diego's Jack Murphy Stadium, Game 4 of the NLCS ended when Padres first baseman Steve Garvey hit a dramatic two run home run off of Lee Smith.

"Deep right field, way back. Cotto going back to the wall...it's gone! Home run Garvey! And there will be tomorrow!" - Drysdale on the call. The Padres, who rallyed from a 2-0 deficit in the best-of-five series against the Cubs wound up winning the decisive Game 5 the next day (thus, winning their first ever National League pennant).

In 1986, he married Naismith Memorial Basketball Hall of Fame player Ann Meyers, who took the name Ann Meyers-Drysdale. It was the first time that a married couple were members of their respective sports' Halls of Fame. Drysdale and Meyers had three children together: D.J., Drew, and Darren.

On September 28, 1988, fellow Dodger Orel Hershiser surpassed Drysdale when Hershiser finished the season with a record 59 consecutive scoreless innings pitched. In his final start of the year, Hershiser needed to pitch 10 shutout innings to set the mark - meaning not only that he would have to prevent the San Diego Padres from scoring, but that his own team would also need to fail to score in order to ensure extra innings. The Dodgers' anemic offense was obliging, however, and Hershiser pitched the first 10 innings of a scoreless tie, with the Padres eventually prevailing 2-1 in 16 innings. Hershiser almost did not pitch in the 10th inning, in deference to Drysdale, but was convinced by the Hall of Famer to take the mound and try to break the record. When Hershiser broke Drysdale's record, Drysdale went to hug the man who just broke his record and told Hershiser "Oh, I'll tell ya, congratulations...And at least you kept it in the family."

Drysdale also called Kirk Gibson's memorable walk-off home run in game one of the 1988 World Series for the Dodgers Radio Network.

Don Drysdale died of a heart attack in his hotel room in Montreal, Canada where he had been broadcasting a Dodgers game in 1993. Drysdale was found dead by radio station employees sent to look for him when he was late for his scheduled broadcast. After Drysdale missed the team bus, hadn't shown up about two hours before game time, and didn't answer his telephone, the hotel staff went in and found him face down, near his bed. The coroner estimated that he had been dead for 18 hours. Soon afterwords, Drysdale's broadcasting colleague Vin Scully, who was instructed to not to say anything on the air until Drysdale's family was notified, announced the news of his death by saying "Never have I been asked to make an announcement that hurts me as much as this one. And I say it to you as best I can with a broken heart." Fellow broadcaster Ross Porter told his radio audience, "I just don't believe it, folks." Drysdale was replaced by Rick Monday in the broadcast booth.

Drysdale's body was cremated at Forest Lawn Memorial Park Cemetery in Glendale, California.