Bucknell set a school record for points in an overtime period with 25. The previous high was 20 against Hofstra in 1987.
The Bison scored just 18 points in the first half and 29 in the second.
Bucknell scored the first six points of overtime and converted 13 of 14 attempts from the free throw line.
K.J. Rose led Fairfield (2-4) with 26 points and Marcus Gilbert had 17.
Gilbert gave Fairfield a 47-41 lead with 2:30 left in regulation. Hass answered with a 3-pointer and J.C. Show nailed a 3 on its next possession to tie the game at 47 with 1:21 left. Fairfield's Tyler Nelson missed a shot at the buzzer.