During his career, Pulli officiated in four World Series (1978, 1983, 1990 as crew chief, and 1995), six National League Championship Series (1975, 1979, 1986, 1991, 1993, and 1997), four National League Division Series (1981, 1995, 1996 and 1998), and two All-Star games (1977, and 1988 as crew chief). He also was the first base umpire in the April 8, 1974, game in which Hank Aaron broke Babe Ruth's home run record.