Drago made the majors when he was picked by the Royals in the expansion draft, and he became the ace of their struggling staff. Improving with the rest of the team, he had his best season in 1971 (17-11, 3.01), but his record suffered when the team declined in 1972 (12-17 despite a 2.99 ERA). Boston acquired him for 1974, and in their AL championship season in 1975 he was their bullpen ace with 15 saves. He saved Games Two and Three as the Red Sox swept the A’s in the ALCS, but lost Game Two of the World Series in the ninth inning on a Ken Griffey double. His three scoreless innings of one-hit ball in Game Six kept Boston in the game, and they won on Carlton Fisk‘s famous homer in the 12th inning.
Traded to California for 1976 and then to Baltimore in mid-1977, he returned to the Red Sox for 1978 and had his last good season in 1979, going 10-6 with 13 saves.