New York — Unselfish basketball is at the heart of UConn’s success.

The Huskies fully embrace their all-for-one and one-for-all mentality.

They put their team-first game on display in Thursday’s Big East tournament quarterfinal win over ninth-seeded Xavier at Madison Square Garden.

They overwhelmed the Musketeers in the second half, blowing open a tight game and closing out the 87-60 victory with an impressive 40-18 blitz.

Along the way, they set program records in league tournament play for assists (a season-high 29) and field goal percentage (.583).

They moved the ball around like a hot potato until they found an open shooter. Five different players had four assists or more.

“We always try to be so unselfish out there and really just try to play for each other,” redshirt sophomore Alex Karaban said. “That’s just what makes this team so special, that’s what makes this team so fun to play for.”

In another sign of their unselfishness, the Huskies shared the scoring load, with six different players hitting double figures. Tristen Newton and Donovan Clingan led the way with 13 points apiece while Karaban, Cam Spencer and Samson Johnson each chipped in 12 and Stephon Castle added 10 points and a team-best eight rebounds.

“We have a pretty deep team, so I feel we can just run teams out of the gym like that,” said Castle. “The defense can’t (focus) on one person.”

Top-seeded UConn (29-3) will play No. 5 St. John’s, a 91-72 winner over No. 4 Seton Hall, in the tournament semifinals at 5:30 p.m. Friday.

“We’ve got to be ready to go from the jump,” Clingan said. “I’m really excited for what this team is going to do. It’s a huge opportunity. … I know everyone in this locker room is very hungry and very ready to go.”

Once the Huskies found their lethal groove on Thursday, the outcome was no longer in doubt.

A tight five-point lead (47-42) with 13 minutes left turned into a blowout when the Huskies hit their stride.

They scored almost at will in the second half, sinking 22 of 28 field goal attempts, or a sizzling 78.3%.

“I’ve never seen anything like that before,” Karaban said. “It’s like (NBA) 2K numbers.”

At one point, Clingan scored 11 straight points inside to help fuel a game-changing 17-2 spurt that pushed the gap to 75-49. He shook off an early funk to be a factor in the second half.

UConn’s lock-down defense limited Xavier (16-17) to 34.4% overall. The Huskies dominated the boards, holding a 43-29 edge.

Coach Dan Hurley emptied his bench in the final minutes.

The game started poorly for the Huskies, who quickly fell into a 10-0 hole. An unhappy Hurley uncharacteristically made two substitutions before the first media timeout, replacing Castle and Clingan with Samson Johnson and Hassan Diarra.

UConn’s two reserves helped spark a 13-0 run and into the lead.

The game remained fairly even for a while. The Huskies went into halftime with a 34-33 edge, a good sign considering the Huskies were 25-0 when leading that the break.

Hurley encouraged his team to raise its intensity level, and they responded.

They played up their standard of excellence in the second half, never trailed and led by double digits for the final 11 minutes.

“This is a playoff game,” Hurley said. “When you’re trying to end the other team’s Big East season or team’s season, you’ve got to be absolutely on point. The execution has got to be on point. The effort and the intensity and the attention to detail, it’s all got to be there.

“Just think it took us a half to get going, but also credit Xavier.”

Now it’s on to the Big East semifinals that will be played before a sold-out crowd. Red-hot St. John’s (20-12) has won six straight.

The Huskies are determined to keep advancing and pursuing the program’s first Big East tournament title in 13 years.

“We’re confident that we’re the best team in the country if we play to our standard,” said Spencer, who had a career-high eight assists. “I think the second half was a great example of how unselfish we are and how well we play together.

“Any team can be beaten on any given night. We have to do the little things well and come ready to play, and I think we’re pretty confident that we’ll come out with the win.”

g.keefe@theday.com