Gibson, who scored 30 against the Bulldogs in their last matchup, was 11 of 17 from the field and hit a game-high nine free throws for the Pioneers, who shot 56.8 percent (25 of 44) overall.
Swidowski was 5 of 5 from the field and knocked down both of his 3-point attempts.
Sacred Heart (13-14, 7-7 Northeast Conference) led 20-16 in the first half before using a 14-4 run to take a 34-20 advantage into halftime.
The Pioneers pushed that lead to 59-31 behind a Gibson layup with 9:54 left to play.
Alex Francis was the only Bulldog in double-figures with 16 as Bryant (2-24, 1-13) shot just 36 percent (18 of 50) from the field, including 4 of 25 from deep.