If Boston College wants to get to TD Garden and have a chance at winning the Hockey East tournament, the Eagles will need to beat Vermont in a Game 3.

The Catamounts dug themselves out of an early 2-0 hole, beating the third-ranked Eagles, 4-2, on Saturday night at Conte Forum to even the best-of-three series. Brendan Bradley scored the winning goal, knocking in a rebound with 8:40 left in the third period. An empty-net goal by Rob Darrar with 0.4 seconds left sealed it.

It’s the second year in a row that the teams will play a third and deciding game at Conte Forum for a spot in the tournament semifinals. A year ago, Vermont won Games 2 and 3 to complete the comeback. The Catamounts will look to do the same this year against top-seeded BC (25-6-5), which has been upset in the quarterfinals each of the past two years.

“We had it 2-0 early in the game, just where we wanted, got a good start. But they hung in there. Now it’s a winner-take-all third game tomorrow afternoon,’’ BC coach Jerry York said. “We’ll need to play better to advance.’’

It took a while for No. 9 seed Vermont (15-21-3) to figure out Thatcher Demko — who shut out the Catamounts on Friday — but they scored twice on him in the second period to tie the game at 2. Brian Bowen tipped in a long shot by Rob Hamilton with 17:10 remaining to cut the lead in half, then Liam­ Coughlin, a freshman from South Boston and Catholic Memorial, flipped the puck past Demko on the glove side to tie the game. It was Bowen’s fourth goal of the season and Coughlin’s third. Coughlin also assisted on Bowen’s deflected goal, and on Darrar’s empty-netter.

“I usually think pass first, but tonight I thought I should take the shot, see what happens. It came out well,’’ said Coughlin, one of six Catamounts who did not suit up for Game 1, but were needed on Saturday because of injury and illness.

Facing elimination and playing with the required desperation, the Catamounts needed a strong second period, because just like Friday, the Eagles had a flying start. This time it was Austin Cangelosi, who had a goal and two assists in Friday’s 3-0 win. With BC on a power play, Cangelosi was parked in front of the Catamount goal, and was able to poke the puck across the line after an initial shot by Scott Savage from just inside the blue line. Savage’s shot was stopped by Packy Munson, but Cangelosi muscled­ his way through a crowd to finally nudge the puck in, with Munson sitting on his backside. The goal was upheld on review, and gave BC a 1-0 lead with 16:11 remaining. Friday’s first goal came 4:14 into the game.

No review was needed on BC’s second goal, with Alex Tuch also the beneficiary of a second-chance opportunity. A long-range Eagles shot was blocked by Munson and trickled out to Tuch, who whizzed a second shot past the Vermont goaltender for a 2-0 lead. It was Tuch’s 14th goal of the season.

Munson, a freshman making his first postseason start, finished with 43 saves as the Eagles outshot Vermont, 45-31.

With those first 20 minutes, Demko extended his consecutive periods against Vermont without allowing a goal to six, dating to a 4-1 regular-season win in Burlington on Feb. 20, when the Catamounts scored their lone goal in the first period. Demko blanked them for the final 40 minutes of that game, then posted his 10th shutout of the season on Friday.

He saw plenty of action in the first period, stopping Travis Blanleil from point-blank range, then stood his ground during a massive pile of bodies in his crease, with the Catamounts trying to literally push the puck – and Demko – into the net. No luck. But their fortunes would soon change.

Now it’s on to Sunday’s game at 4 p.m. With No. 2 seed Providence, No. 4 UMass-Lowell, and No. 6 Northeastern earning their Garden tickets with victories on Saturday night, only one spot remains.

“I think we gained some confidence tonight. Last night, at times, we were shocked by their speed and skill. Despite going down, 2-0, I thought we adjusted to it. Things weren’t as shocking to us,’’ Vermont coach Kevin Sneddon said. “The situation is still the same tomorrow. Our backs are still against the wall. We have to play with desperation, leave it all out there, and hope that it’s good enough. There will be two hungry hockey teams that want to get to the Garden.’’