His best season was 1962, when he posted a 23-12 won-loss record. He pitched 298-2/3 innings, striking out 176, while walking 57. His 23 victories led the American League that year.
In five World Series (1960–64), Terry posted a record of 2-3, 31 strikeouts and a 2.93 ERA. Both wins came in the 1962 World Series (of which he was named MVP) against the San Francisco Giants, including a 1-0 shutout in Game 7 over Giant ace Jack Sanford. That game—and thus the Series—ended with Yankee second baseman Bobby Richardson catching Willie McCovey's line drive with Willie Mays on second and Matty Alou on third; had the ball been hit a foot or so to either side, Richardson could not have caught it and San Francisco would have scored two runs and won the Series.
After baseball, Terry became a professional golfer. Based on his status as a PGA of America Sectional Champion, he qualified for and played in four PGA Tour events in 1981 and 1982. In 1986, he started playing on the Senior PGA Tour. His best finish was a tie for 10th at the 1989 Showdown Classic.