Virginia (29-7) advances to the Elite Eight for the first time since 1995.
Niang, who came in averaging 20.2 points per game, went for a game-high 30, but the 6’9” senior had to go to the bench for a stretch in the second half when he picked up his fourth foul with 13:11 to go.
At that point, Iowa State (23-12) had cut the Cavs’ lead to 54-46, and the Cyclones had a partisan crowd in the United Center in Chicago on their feet.
UVA went on a 9-2 run over the next 4:02 to open up a 15-point lead, and ISU coach Steve Prohm called timeout to re-insert Niang.
But the margin never got closer than 10 the rest of the way as Virginia made its last six shots from the field in the final 3:25.
Virginia got 23 points and eight rebounds from Anthony Gill, and Mike Tobey contributed 18 points and seven rebounds off the bench for the ‘Hoos, who shot 56.1 percent (32-of-57) from the field.
London Perrantes had six points and nine assists for Virginia, which had 26 assists on its 32 made baskets on the night.
Malcolm Brogdon had 12 points and five assists.
Niang’s 30 came on 11-of-20 shooting from the field. The Cyclones shot 51.9 percent from the field (27-of-52).
UVA had a 33-24 advantage in rebounds, with a 7-2 edge in offensive rebounds and a 12-3 margin in second-chance points.
The Cavs outscored ISU in the paint 52-36.