Connolly attended the University of Massachusetts Amherst, and signed with the Red Sox before the 1961 season. In his two-season MLB career, Connolly posted a 6–12 record with 118 strikeouts and a 5.88 ERA in 42 appearances, including 19 starts, one complete game, one shutout, and 130.0 innings of work. During his minor league career, he struck out 192 batters in 167 innings in 1962 (a season he split between the Class D New York–Penn League and the Class B Carolina League), and he fanned 157 men in 162 innings in 1963 pitching in the Double-A Eastern League.