Eaves had 15 points, eight rebounds and three steals for the Mountaineers. Tommy Spagnolo added 10 points and eight rebounds.
Chris Bilbo's 3-pointer for Troy (9-13, 4-9) capped the scoring with less than a second left.
The Trojans never led after an early 12-11 advantage but challenged throughout the second half, culminating at 59-all on Musa Abdul-Aleem's 3-pointer with 3:48 left. Abdul-Aleem missed a pair of 3s in the final 2:30 that allowed the Mountaineers to pull away.
Kevin Thomas led the Trojans with 13 points, Bilbo scored 12 and Abdul-Aleem 11.