Sometimes clichés just fit like a glove.

A two-goal lead was the most dangerous lead in hockey Thursday, as Boston University dominated Providence in shots and possession for the first 46 minutes, only to surrender a 2-0 lead in the last 14 minutes of regulation.

Friar forward Chris Chaput — a healthy scratch in last weekend’s win against Maine — added the game winner at 3:33 of overtime to make it a 3-2 win for Providence in front of 2,267 fans at Walter Brown area. It was a classic never-say-die performance, especially by Friar goalie Nolan Schaefer, who made 42 saves.

Peter Fregoe had a goal and an assist for the Friars (11-7-1, 5-6-1), who were outshot 20-3 in the second period and who could not muster a single shot on goal for the first six minutes of the third period until Fregoe lit the lamp to spark the team. Mark Mullen and Brian Collins had a goal apiece, and Bryan Miller added a pair of assists for the Terriers (13-7-2, 7-5-0) in a losing effort.

“I’d rather get outshot and win ugly, and that’s what we did tonight,” Friar coach Paul Pooley said. “Nolan Schaefer had a huge game tonight. At this point of the year, it doesn’t matter how you get the wins, you just have to get the ‘W.’ I’ll take this one any day.”

“I thought we dominated the first two periods but didn’t dominate on the scoreboard,” Terrier coach Jack Parker said. “We let them hang around, and they kept hanging around because of how well Schaefer played.

“But also we had a lot of good chances that we thought were going to go into net, and we didn’t make sure,” added Parker. “They kind of rope-a-doped us — outshooting them badly in the first two periods, and then it’s 11-11 in the third and they get a goal and get jacked up. The goals they got were just absolute critical mistakes on coverage.”

BU dominated territorially for much of the first period, though the teams traded chances over several power plays. Ultimately, the Terriers broke on top with all of two-tenths of a second left in the period.

D-man Bryan Miller raced up ice on the right wing before taking a shot that Schaefer stopped with a pad. Trailing the play, Mark Mullen almost had the rebound slip behind him, but he wheeled and fired the puck off the far post and in just before the buzzer sounded.

The momentum from the buzzer-beater carried into the second period, when the Terriers played one of their better periods of the season, suffocating the Friars territorially and piling up almost seven shots for every one that they surrendered.

Peter Zingoni did have one good chance at 8:15 for the Friars, when a pass off the boards left him alone with BU goalie Sean Fields, but the Terrier junior made the blocker save. The Terriers looked to have a goal at the 12-minute mark when Justin Maiser’s redirect of a Whitney shot hit a post and headed for the net. Several Terriers lifted their sticks, only to see the puck deflect through the crease, missing the other post by inches.

On a power play at 18:18, there was another slapshot and redirect, and this time the Terriers’ aim was true. Brian Collins got a piece of Freddy Meyer’s slapshot, and the puck dribbled over Schaefer’s arm and in for the 2-0 lead.

After the ominous shooting drought to start the third period, Providence scored on its second shot of the third stanza on an excellent playmaking read by Devin Rask. The left winger received a pass going toward the goal line and somehow knew that Fregoe was trailing the play behind him and to his right. Fields was lured to the side of the net, and when the pass came out in the slot, Fregoe had ample net to hit. That made it 2-1 at 6:35.

BU very nearly regained the two-goal cushion at the nine-minute mark when Frantisek Skladany crashed the net to redirect another Whitney shot, but Schaefer got himself in the right place. With the Terriers dominating in the PC end, he was forced to make several saves amidst traffic.

“I think my more important saves have been the ones in traffic that I’ve really been having trouble with,” Schaefer said.

“He made a couple of great saves on seeing-eye shots from the point,” Parker said.

Providence tied the game with 6:26 remaining when Stephen Wood took a big 30-foot slapshot, falling down in the process. Fields had a clear view of it, but the puck knuckled down and appeared to beat him five-hole to tie it.

“I think when we got the first goal, we got a little bit of belief,” Pooley said. “When we got the second goal, we were sky-high.”

Referee Scott Hanson put away the whistle from there on in, ignoring a few brutal BU hits into the boards as well as some clutching and grabbing by the Friars.

Chaput’s overtime game-winner came just after the Terriers’ umpteenth close-but-not-quite scoring opportunity. Ryan Whitney skated in on the left wing and took a good shot. Skladany was well-positioned for the rebound, except for the fact that his stick had just been knocked out of his hands.

Freshman Torry Gajda picked up the rebound and set up Chaput for the breakaway. It looked as if Fields guessed that Chaput would deke and go low on the glove side, but Chaput shot it up and in on the stick side as Fields sprawled to his left.

“There were some big goals in high school, playing at Mount [St. Charles in Rhode Island], but I’d have to say that this was up there as one of the big ones,” Chaput said.

“It’s a great feeling to see your team pick up and come back like that,” Schaefer said. “Any time you can win in BU’s barn, it’s just a great experience.”

“We played real well tonight,” Parker said. “You can’t call that a bad loss. If there’s such a thing as a good loss, that was a good loss. But it hurts us in the league and hurts us overall. It’s hard to swallow.”

BU has the rest of the weekend off and will play archrival Boston College in a home-and-home series next weekend. Providence hosts New Hampshire on Saturday night.