Erick Green, the nation's third-leading scorer, missed a jumper at the buzzer as the Hokies (7-1) lost for the first time.
Staten's winning field goal was his only one of the day. He took an inbounds pass from under the basket and waltzed through a clutch of Hokies for a layup with 5 seconds left. He had missed a similar shot 4 seconds earlier, but the ball hit a Hokies player, giving possession to the Mountaineers (4-3).
Virginia Tech coach James Johnson immediately called a timeout. He set up a play with 3.4 seconds left that got the ball to Green from the sideline in front of the Hokies' bench. The two-time Atlantic Coast Conference player-of-the-week took several dribbles and put up a shot that hit iron at the buzzer.
Green scored a game-high 23 points.
Kevin Noreen contributed his first double-double (14 points, 12 rebounds) for West Virginia. The scoring total was his highest in three injury-plagued seasons -- he was awarded a medical redshirt for 2011-12) -- and he also made the first two 3-point shots of his career.
Noreen was part of a bench that outscored Virginia Tech's reserves 36-4. He was 6 of 10 from the floor, making 2 of 3 3-pointers. Another bench player, Eron Harris, added 10 points and five rebounds in 26 minutes.
Transfer Aaric Murray, a junior from La Salle, was the Mountaineers' leading scorer. The starter had 15 points and seven rebounds, and hit 2 of 3 3-pointers.
After scoring nine points in the first half, Green exploded for 14 in the second. Jarell Eddie, who came in averaging 17-plus points, was held to five largely because of foul trouble. Robert Brown contributed 21 points.
West Virginia connected on 10 of 24 3-pointers (41.7 percent), the most it has made since getting 10 against Missouri State on Dec. 22, 2011. The Mountaineers were averaging 3.3 per game this season and hitting just 23 percent.
The Hokies, who came in averaging 85 points per game and were making 40.3 percent from 3-point range, dropped to 27.8 percent (5 of 18) behind the arc in the second half.
West Virginia had a 49-38 rebounding edge, including 23-13 on the offensive end. The Mountaineers outscored the Hokies 18-10 in second-chance points.
The last time the two border rivals met was the 2003-04 season, when Virginia Tech swept the series. West Virginia leads the all-time series 47-29.