Nelson made four 3-pointers as did Marcus Gilbert, who scored 16 points. Jerome Segura added 14 points for the Stags (6-5), who have won six of their last eight.
The Stags shot 48 percent but made 17 of 32 3-point attempts for 53 percent.
Ryan Frazier scored 20 points, Chris Haas 19 and Nana Foulland 15 for the Bison (3-8), who have lost seven straight heading into their Patriot League opener against Navy.
The Bison finished the first half on a 25-13 run and trailed by two at halftime. Nate Sestina's 3-pointer to open the second half gave them the lead. Fairfield responded with four straight 3-pointers and Gilbert finished the 14-0 run with a dunk.
A 10-run gave Fairfield an 86-67 lead. Bucknell was within five before the Stags finished with three free throws and a Nelson layup.