Despite the Stags doing their part at the free throw line to escape with a victory, the Bison kept pressure on Fairfield in the final minutes.
After Chappell knocked down a pair at the free throw line, Ryan Frazier buried a trey to trim the Stags lead to 60-49.
However, the Stags converted a three-point play on their next trip down the floor and made enough free throws to keep the lead around double digits.
The Bison pulled within eight points on two occasions in the final minute but could not pull closer.
Cameron Ayers and Steven Kaspar started to find their way through the lane for layups as the game progressed.
"I thought Cam played exceptionally well on both ends of the floor," Paulsen said.
Bucknell kept the deficit within two possessions early in the second half, where a made basket and a turnover could have given them a chance to tie the game or take the lead.
Trailing by six, 36-30, Dom Hoffman pulled down a board off of a missed Stags layup and Ayers knocked down a jumper at the other end to pull the Bison to within four.
Hoffman cleaned up another miss in close and got the ball into Kaspar's hands. He knocked down a pair of free throws after a drive into the lane.
However, after the Bison cut the lead to two, 36-34, Fairfield's Steve Smith scored six of his seven points.
An inbounds play worked its way to Smith, who calmly stroked a 3-pointer and then repeated the motion after a missed Bison jumper to quickly extend the Fairfield lead to eight points.
The Bison trailed early in the game before a 10-0 run flipped the tables. Taking advantage of a series of Fairfield misses from the perimeter, the Bison found their mid-range and long-range games with Chris Hass hitting a jumper, and Ayers and Hass each hitting threes.