The signs were right there from the outset when Notre Dame made six of its first seven shots to open a double-digit lead on Virginia. The ACC’s smoothest offense was going to meet the challenge of its stingiest defense.

The 22nd-ranked and third-seeded Fighting Irish trailed for only the first 39 seconds as they rolled past a No. 21 Cavaliers team having a distinctly off night in a 71-58 quarterfinal win before 17,732 at Barclays Center.

Notre Dame (24-8) shot 52 percent from the floor in each half as it garnered its first win against Virginia since 1981, a run of 10 straight, including the past five as conference foes. “It’s nice to get the first one when the stakes are really high,” Notre Dame coach Mike Brey said.

The Irish will be making their third straight trip to the semifinals and will meet second-seeded Florida State Friday.

“I think we’re really hungry and motivated to play these guys. It’s been a tough route playing them in the past, so I think we wanted it more,” said Notre Dame’s Bonzie Colson, who finished with 21 points and 10 rebounds. “We got off to a great start. That’s something Coach Brey has been emphasizing, great starts on offense.”

Notre Dame led 32-26 at halftime and opened the second half with an 11-0 run in which five players scored. Virginia never got closer than 68-58.

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“We were outplayed today. They played well, and we didn’t have one of our better games,” Virginia coach Tony Bennett said. “Their ball movement was terrific tonight. The pace on their cuts was good, and they had us behind the play. When we’re at our best defensively, we’re there, and we’re anticipating.”

Matt Farrell had 14 points and Steve Vasturia and V.J. Beachem scored 12 each for the Irish.

Devon Hall and Darius Thompson had 12 points each for Virginia (22-10), but star London Perrantes had only three points, shooting 1-for-9, and Kyle Guy, who had 20 points in a second-round win the night before, was 0-for-8 shooting and didn’t score.

“We were great on the defensive end, rebounding and playing without fouling,” Colson said. “That’s something we need to keep doing.”