After West Virginia dominated the boards to lead at halftime, coach Pat Kennedy told his weary Florida State team to step it up.
Florida State, playing for the second time in three nights, responded with 14 offensive rebounds that led to 22 second-half points, and its defense held West Virginia to 36.5 percent shooting for a 76-71 win Wednesday in the third round of the NIT.
"Our game plan was to be inside," said Randell Jackson, who had 19 points. "We wanted to just pound it in there. If we miss the shot, get the rebound. We didn't do that in the first half. The first half was terrible."
Florida State (19-11), playing in the post-season for the first time in four years, advanced to the semifinals in New York and plays the winner of Friday's Connecticut-Nebraska game.
James Collins scored 24 points, and injury-plagued Corey Louis came off the bench for 14 for Florida State. Louis, twice hobbled by injuries this season, scored 10 points in the second half.
West Virginia (21-10) lost a last chance when Brent Solheim was called for an intentional foul with 2.9 seconds left. Jackson made both free throws, and the Seminoles regained possession as time expired.
The Mountaineers, the Big East's highest-scoring team at 81 points a game, lost for the 10th time in 15 games when scoring fewer than 80.
Seldon Jefferson, West Virginia's senior co-captain and leading scorer, was held to 4-of-18 shooting for 12 points. Adrian Pledger led the Mountaineers with 18 points.
The Mountaineers led by 10, the biggest lead of the game, 3:46 into the second half before the Seminoles came back.
"I had to get after them to play harder," Kennedy said. "If you let your guard down at this level, you're going to get spanked."
Mountaineers coach Gale Catlett, whose team beat North Carolina State on Monday, took some of the blame for bringing in fresh players when the Mountaineers led by 10.
"I made a mistake when I subbed in a lot of fresh guys. I broke up our chemistry," he said.
The Mountaineers led 39-35 at the half after Solheim sparked an 8-0 run in the final 2:43.
West Virginia used a 26-15 advantage on the boards in the first half to lead despite shooting 37.8 percent. The Mountaineers shot 35 percent in the second half.
They finished ahead in rebounds, but the Seminoles' putbacks were the difference.
"They got some loose balls off the offensive boards, which created more opportunities, which turned into second-chance points," Jefferson said. "They did a great job sticking to their game plan."