Jevon Carter scored 17 of his 23 points in the second half for West Virginia (8-1), and the point guard added 10 rebounds and seven assists.
Devon Hall finished with 19 points and six assists for Virginia (8-1), who stayed close thanks to an 18-point second-half outburst from top shooter Kyle Guy.
Guy started 0 of 6 from the floor and went scoreless until 13:52 remained in the game before making three consecutive 3-pointers in a 64-second span to put the Cavaliers ahead 41-39.
While the Cavaliers committed 15 turnovers -- still shy of the number West Virginia is accustomed to forcing -- two by point guard Ty Jerome in the final 1:28 were costly. With his team down by a bucket, he was called for traveling in a corner trap, and on the next possession his pass was stolen by Daxter Miles.
Miles scored 12 points as West Virginia's big three provided 57 of the team's 68 points.
The Mountaineers shot 42 percent overall and got 10 of their 21 baskets from 3-point range.
Virginia shot 41.3 percent from the floor, including 9 of 23 from deep, but made only one basket over the final 4:50.
West's 3-pointer put West Virginia ahead 54-51, and his midrange jumper broke a 56-all tie.
West Virginia, after leading for more than 17 minutes in the opening half, settled for a 29-26 lead at the break. Hall hit a 3-pointer and De'Andre Hunter made two free throws after being fouled on a scramble with 0.7 seconds left.
NOTES: West Virginia averaged 93 points during its previous seven wins. ... In a pregame ceremony, the Mountaineers recognized G Jevon Carter for becoming the school's career steals leader. ... West Virginia took a 10-9 lead in the all-time series.