NEW YORK -- Something had to give for Mike Brey's Notre Dame Fighting Irish on Thursday night when they faced off against Virginia in the quarterfinals of the Atlantic Coast Conference tournament.

On one hand, Brey's team had yet to beat the Tony Bennett-led Cavaliers since joining the ACC back in 2014. On the other, Notre Dame has enjoyed great success in the ACC tournament, advancing to at least the semifinals every year since becoming a member.

The strong postseason record continued as third-seeded Notre Dame advanced to the semifinals with a 71-58 victory over sixth-seeded Virginia at Barclays Center.

It took the 22nd-ranked Fighting Irish six tries, but they finally conquered the 21st-ranked Cavaliers.

"I thought we defended fabulously for 40 minutes to win tonight," Brey said of his team. "Getting off to a good start in the first half and the beginning of the second half I think was a key. But I'm really proud of our defense to hold them under 40 percent field-goal percentage.

"We were smart offensively. We had the floor spread pretty good. It's a great win for us. Obviously, we've not had much success against the Virginia program. It's nice to get the first one when the stakes are really high."

Notre Dame (24-8) led by as many as 17 in the second half as it doubled a six-point halftime lead five minutes into the second period. Bonzie Colson led the way with 21 points and 10 rebounds.

"I think as a team we wanted it bad," Colson said. "We just wanted to stick with what we were doing on both sides of the floor, rebounding, getting balls. Other side of the floor, we just integrate rhythm. (My teammates) were hitting great shots and just played at a great tempo on the offensive end."

Matt Farrell scored 14 points, while V.J. Beachem and Steve Vasturia added 12 apiece for the Fighting Irish, who meet No. 17 Florida State in Friday's semifinals.

Virginia (22-10) struggled to find its touch as it shot 38.6 percent from the field. Devon Hall and Darius Thompson led the Cavaliers with 12 points apiece.

"First, credit to Notre Dame. We were outplayed today," Bennett said. "We were behind in the play. They really were moving the ball well. They're hard to guard. They played well, and we didn't have one of our better games. We have to learn from it but pick up and move on and just were a bit lethargic."

Notre Dame shot 52.2 percent and got 34 points in the paint against the Virginia packline defense.

"You learn from this," Bennett added. "We talked about it in the locker room after. We've got whatever little bit of time now. We recover. We rest. But we prepare as well as we can in practice and tighten up. We weren't as sound as we've been in the past. A formula for our success has been we've taken care of the ball, and we've shot it pretty well."

The Cavaliers trailed by as many as 10 during the first 20 minutes as they allowed Notre Dame to shoot 52 percent from the field. The Fighting Irish led 32-26 at halftime.

NOTES: This was the first meeting between the teams in the ACC tournament. ... Each team has won an ACC tournament title in the past three season with Virginia winning in 2014 and Notre Dame wearing the crown in 2015. ... Notre Dame managed just nine assists in the game, five from G Steve Vasturia and four from G Matt Farrell. ... G Ty Jerome recorded half of Virginia's 12 assists.