Stuckey hit 12 of 13 from the foul line and added seven assists. Williams finished with 13 points and nine rebounds for the Eagles (7-7, 1-1 Big Sky), who broke a six-game losing streak to the Grizzlies (7-8, 1-1).
Williams' two foul shots gave Eastern its biggest lead, 72-65, with 44.7 seconds left.
Montana clawed to within 72-69 with 25 seconds remaining after a basket by Cameron Rundles and a steal and layup by Jordan Hasquet. Montana's Stuart Mayes stole the ensuing inbound pass, but the Grizzlies missed a 3-point attempt that would have tied it.
Williams grabbed the rebound and was fouled with 8.3 seconds left, making both foul shots and securing the Eastern win.
The Grizzles had an early 11-0 run, taking a 27-14 lead on Matt Martin's 3-pointer with nine minutes left in the first half. It was one of four first-half 3-pointers for Martin, who finished with 16 points but was held scoreless in the second half.
Eastern rallied behind Stuckey, who scored seven of his 11 first-half points during a 12-3 burst that pulled the Eagles to within 30-26 with 6:20 remaining. Brandon Moore came off the bench to score 12 for the Eagles, whose reserves outscored Montana's second unit 35-14.
Eastern finished 23 of 29 from the foul line, 19 of 23 in the second half.
Andrew Strait had 15 points and eight rebounds before fouling out for Montana. Hasquet added 14 points and eight rebounds for the Grizzlies, who shot 56 percent from the floor in the first half and just 39 percent in the second half.