He paused, though, as the ball drifted back, caromed off the backboard, and fell through the net — a huge bounce that helped seal the Bulldogs’ 63-59 upset of top-seeded Syracuse last night in the West Regional semifinals.

Veasley followed his fortunate three with a tip-in as the Bulldogs scored 11 straight points and became the latest mid-major team to knock off a top seed in the NCAA Tournament.

Now, after reaching the regional finals for the first time in school history, Butler is one win from going home to Indianapolis for the Final Four.

“I was headed down the court on defense because I figured it was going to go over the top of the backboard. But I looked back and it came down and went through,’’ Veasley said. “That was a H-O-R-S-E shot. I’ve never made a shot quite like that.’’

Veasley pumped his fist and grinned as he continued toward the other end. It was fitting that he was already headed back on defense. Instead of Syracuse’s vaunted zone controlling the game, Butler’s pesky man-to-man defense was the difference as the Bulldogs scrapped through poor shooting and won their 23d straight game.

“We said this word over and over in Indianapolis, and that word is ‘resolve.’ These guys have resolve,’’ Butler coach Brad Stevens said. “It’s hard to measure, but they’ve got it.’’

The Bulldogs (31-4) certainly did in the last five minutes, holding the Orange without a point from the time Syracuse went up by 4 with 5:23 left until a too-little-too-late layup with 35 seconds remaining.

Gordon Hayward scored 17 points and started the celebration while dribbling out the clock after the Bulldogs forced Syracuse into its 18th turnover.

The Orange (30-5) made just three more field goals than turnovers in another loss in the round of 16. Syracuse hasn’t played in the regional finals since winning the 2003 national title.

“The game was a story of turnovers. They didn’t make turnovers,’’ Syracuse coach Jim Boeheim said. “They were really good with the basketball. We just had 18 turnovers and you can’t give away that many possessions.’’

Veasley finished with 13 points and three steals. Ronald Nored finished with five steals and hit a 3-pointer to start the decisive run.

“Under any circumstance, I think we’re poised. You have to be tough,’’ said Nored, whose 3-pointer with 3:14 left cut Syracuse’s lead to 54-53.

Wes Johnson had 17 points and nine rebounds for the Orange, the second No. 1 seed to go down. Northern Iowa stunned top-ranked Kansas in the second round of the Midwest Regional last weekend.

Scoop Jardine added 14 points and five assists and Andy Rautins scored 15, including a 3-pointer to open the second half. That sent the Orange on a 15-4 run that gave them their first lead.

But the sloppy Orange couldn’t overcome all their turnovers, and the 2-3 zone that so many wondered whether Butler could crack was no match for the Bulldogs’ sharp shooting in the final minutes after Syracuse had taken a 54-50 lead with 5:23 left — then didn’t score again for almost five minutes.

After Nored’s 3-pointer cut the deficit to 1, Matt Howard scored inside to put the Bulldogs back ahead and then Veasley got his fortunate bounce to put Butler up, 58-54.

Veasley added a tip-in on Butler’s next possession, and the Bulldogs held on.

Next up for Butler is Kansas State tomorrow in the regional final.