Marvin Binney scored 10 points off the bench for the Dukes (6-4), who beat the Mountaineers for the first time since 2003 behind a solid second half that erased a 15-point deficit.
Juwan Staten led West Virginia (4-4) with 13 points and Gary Browne and Matt Humphrey added 10 points each, but the Mountaineers saw their three-game winning streak end during a miserable 20 minutes in which they struggled on both ends of the floor.
West Virginia shot just 28 percent (9 of 32) in the second half, allowing Duquesne to get back in the game.
Jones and Colter led the way, scoring the Dukes' last 15 points to give head coach Jim Ferry his first signature victory since coming over from LIU-Brooklyn last spring.
Ferry inherited a massive rebuilding job after a number of high-profile players revolted against former coach Ron Everhart, now an assistant under Bob Huggins at West Virginia. Everhart spent six seasons at Duquesne before being let go and looked almost uncomfortable wearing a white shirt and gold tie while sitting on the visitors' bench at Consol Energy Center.
The Mountaineers wasted little time making themselves at home, quickly building a 25-10 lead. They clamped down on Duquesne and made it difficult for the Dukes to get into any kind of offense.
Still, it hardly mattered.
Duquesne trailed by 13 at the break before finding its footing. The Dukes pulled within single digits on a jumper by Binney with just under 13 minutes to play and they kept right on coming.
Jones and Colter took over late, with Jones converting a traditional three-point play to give Duquesne its first lead at 50-49. The teams traded baskets for a couple of minutes before a jumper by Colter with 2:02 left put the Dukes up to stay. Colter added a difficult reverse layup on the next trip to put the Dukes up 59-53.
West Virginia's best chance came in the final seconds. Humphrey hit a 3 to get within 59-56 and Duquesne's Sean Johnson missed the front end of a 1-and-1. Humphrey, however, missed a long 3-pointer and Browne was fouled trying to go for the rebound with 11 seconds remaining.
Browne missed the first free throw, then intentionally missed the second. The ball, however, didn't hit the rim, giving possession to Duquesne. Colter was fouled on the ensuing inbounds and made one free throw, snapping West Virginia's three-game winning streak.
The Dukes erupted off the bench in celebration after getting a breakthrough win following a difficult first month of the season that included losses to No. 15 Georgetown and cross-town rival Pittsburgh in the annual City Game.
Despite giving away size at nearly every position, Duquesne outrebounded the Mountaineers 43-39 and outscored West Virginia in the paint 36-20.