Blackshear, a McDonald's All-American, saw in his first action of the season. He suffered a right shoulder injury in October and wore a protective sleeve in the game Saturday, his 20th birthday.
Kevin Jones had 22 points and 11 rebounds for West Virginia (16-10, 6-7). Deniz Kilicli added 17 points and Darryl "Truck" Bryant scored 13.
West Virginia led 63-54 after a Kilicli basket with 10:49 left, but he didn't score again and eventually fouled out. Louisville went to a full-court press to force turnovers and seize the momentum.
Kuric hit a 3-pointer and Russ Smith stole the ensuing inbounds pass and made a layup with 2:21 left to put Louisville ahead 73-71, its first lead since midway through the first half.
Chris Smith and Kuric each sank two free throws in the final 1:19 to offset Jones' 3-point play.
Bryant's 3-point try at the buzzer never hit the net.
The Mountaineers' shooting touch was consistent until the end, when they made just one basket over the final five minutes to lose for the fifth time in six games. West Virginia shot 36 percent (8 of 22) after halftime.
Despite shooting bonus free throws over the final 11 minutes, West Virginia attempted just eight, making four.
Louisville returned from a five-day layoff by hitting five of its first six 3-point attempts. But the Cardinals didn't have much early luck inside the arc, including a missed layup on a 4-on-1 break.
West Virginia held Louisville scoreless over a nearly four-minute stretch in the first half, and Kilicli scored five points during a 12-0 run. The Mountaineers shot 50 percent from the floor in the first half, led by as many as 13 points and were ahead 44-37 at halftime.
The 44 points tied for the most allowed by Louisville in the first half this season.