WVU was forced to foul down three with less than 15 seconds to play following the call, and guard Jeremy Lamb hit two free throws to seal the game.
Senior guard Truck Bryant's 3-pointer was blocked, and Lamb hit a fast-break layup to end the game.
Jones finished with 22 points to lead WVU. Bryant, however, was held to just eight points on 2-of-13 shooting.
The Mountaineers couldn't handle Huskies' freshman center Andre Drummond, who finished with 20 points and 11 rebounds. Lamb had a game-high 25 points.
UConn shot 55.3 percent to WVU's 32.3 percent, and the Mountaineers made only 6-of-24 3-pointers.
Player of the Game
After trailing by five early on, the Mountaineers went on a six-point run off two steals to take a 10-9 lead.
Back and forth action led to a 13-13 game on a Bryant 3-pointer before he and junior forward Deniz Kilicli both left the game with two fouls each.
Without those two on the floor, WVU was actually able to take the lead at 21-16 behind five straight points from Jones.
UConn, however, started to pick the pace of play up and use its size on the inside to bother the smaller Mountaineers.
Jones kept West Virginia in the lead with his outside shooting, which is surprising since he came into the game shooting just 23.3 percent from beyond the 3-point line.
Freshman point guard Jabarie Hinds and Jones scored the next 15 points for the Mountaineers to give them a 31-23 lead with less than four minutes to play in the half.
WVU went into the half up 33-28.
Connecticut shot 57.9 percent in the first half to WVU's 37.1 percent. However, the Mountaineers had a 35-to-19 advantage in shots taken.
WVU did not score in the first four minutes of the second half, and that allowed the Huskies to gain a 34-33 lead on six straight points.
However, Jones scored layups off two offensive rebounds to regain the advantage with less than 15 minutes to play at 37-34.
WVU was able to take a double-digit lead on a 13-2 run to make it 46-36, but an ally-oop dunk by Lamb sparked the crowd at the XL Center. It also sparked the Huskies on a 12-2 run that tied the game at 48-48 with more than six minutes to play.
A deep 3-pointer by Lamb gave the Huskies their first lead since in the first half at 51-48.
The run would continue, as UConn took advantage of Kilicli being out of the game once again due to foul trouble. The Huskies would score 19 of the next 24 points after WVU went on that 13-2 run.
After UConn has taken a 55-51 lead, the Mountaineers went on a small 4-0 run behind two free throws from Kilicli and a dunk in transition from Jones to tie the game.
However, a jumper by Lamb put the Huskies up 57-55, and Kilicli was just 2-of-4 from the line during a small stretch late in the game that allowed UConn to keep its lead.
A putback by Drummond gave Connecticut a 60-57 lead with 1:18 to play.
UConn had nine blocks in the game.