Drysdale was also considered a good hitter for a pitcher. In a total of 14 seasons, he had 218 hits, including 29 home runs, and was occasionally used as a pinch-hitter.
In 1962, Drysdale won 25 games and the Cy Young Award. In 1968, he set Major League records with six consecutive shutouts and 58 consecutive scoreless innings; the latter record was broken by fellow Dodger Orel Hershiser 20 years later. In 1963, he struck out 251 batters and won World Series Game 3 at Los Angeles' Dodger Stadium over the Yankees, 1–0. In 1965, he 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 helped the Dodgers to their third World Championship in Los Angeles. He ended his career with 209 wins, 2,486 strikeouts, 167 complete games and 49 shutouts. He was inducted into the Baseball Hall of Fame in 1984, and had his number 53 officially retired at Dodger Stadium on July 1, 1984. (He was the last player on the Dodgers who had played for Brooklyn.)
Drysdale took part in a famous salary holdout in the spring of 1966 along with Koufax, with both finally signing contracts just before the season opened. This holdout was the beginning of what would eventually become collective bargaining.
While broadcasting for the White Sox, Drysdale generated some controversy while covering a heated argument between an umpire and Sox manager Tony LaRussa. LaRussa pulled up the third base bag and hurled it into the outfield, to the approval of the Comiskey Park crowd, and ensuring his ejection. Drysdale remarked, "Go get 'em, Dago!"
For the Sox, Drysdale broadcast the 300th victory of Tom Seaver, against the host New York Yankees in 1985. His post-game interview with Seaver was carried live by both the Sox' network and the Yankees' longtime flagship television station WPIX.
Drysdale hosted a nationally syndicated radio show called Radio Baseball Cards. 162 episodes were produced with stories and anecdotes told by current and former Major League Baseball players. The highlight of the series were numerous episodes dedicated to the memory and impact of Jackie Robinson as told by teammates, opponents and admirers. Radio Baseball Cards aired on 38 stations, including WNBC New York, KSFO San Francisco and WEEI Boston, as a pre-game show. A collector's edition of the program was re-released in 2007 as a podcast.
Drysdale conducted all of the National League player interviews for the Baseball Talk series in 1988 (Joe Torre did the same for the American League).
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 to take the mound and try to break the record. When Hershiser broke Drysdale's record, Drysdale went to hug him, and said, "Oh, I'll tell ya, congratulations... And at least you kept it in the family."
Well, the crowd is on its feet and if there was ever a preface to Casey at the Bat it would have to be the ninth inning. Two out. The tying run aboard, the winning run at the plate, and Kirk Gibson, standing at the plate. Eckersley working out of the stretch, here's the three-two pitch...and a drive hit to right field (losing voice) WAY BACK! IT'S GONE! IT'S GONE! (After 2 minutes of crowd noise) This crowd will not stop! They can't believe the ending! And this time, Mighty Casey did NOT strike out!!!!
Drysdale married Ginger Dubberly in 1958, with whom he had a daughter, Kelly. They divorced in 1982. On November 1, 1986, he married basketball player Ann Meyers, who took the name Ann Meyers-Drysdale and survived him in death. Drysdale and Meyers had three children together: Don Junior ("DJ") (son), Darren (son), and Drew (daughter). In 1990, Drysdale published his autobiography, Once a Bum, Always a Dodger.
Drysdale was 56 when he died of a heart attack in his hotel room in Montreal, Quebec, on July 3, 1993. Radio station employees were sent to look for him when he failed to make the bus for Olympic Stadium where the Dodgers were to play the Montreal Expos. Hotel staff entered his room and found him face down, near his bed. The coroner estimated that he had been dead for 18 hours.
Drysdale's broadcasting colleague Vin Scully, who was instructed 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.
Among the personal belongings found in Drysdale's hotel room was a cassette tape of Robert F. Kennedy's victory speech after the 1968 California Democratic presidential primary, a speech given only moments before Senator Kennedy's assassination. In the speech, Kennedy had noted, to the cheers of the crowd, that Drysdale had pitched his sixth straight shutout that evening. Drysdale had apparently carried the tape with him wherever he went since Kennedy's murder.
The Donna Reed Show episodes "The Man in the Mask," first broadcast in 1962; "All Those Dreams," first broadcast in 1963; and "Play Ball" and "My Son the Catcher," both first broadcast in 1964. In all four episodes Drysdale played himself, and in "All Those Dreams" he appeared with first wife, Ginger, and daughter Kelly.