CHESTNUT HILL, Mass. — From a literal standpoint, the University of Vermont is separated from the TD Garden by a 215-mile car ride, taking three hours and sixteen minutes down I-89.

From a hockey standpoint, the University of Vermont is now separated from the TD Garden by an inch.

During overtime of the third game of the Hockey East quarterfinals, Mario Puskarich put a shot on Thatcher Demko. The puck ended up on the goal line, spinning like a top. The puck, ultimately, did not cross the line, instead dancing along the goal line before the Boston College defense was able to clear the puck.

Minutes later, Ryan Fitzgerald sealed a Hockey East semifinal berth for Boston College on a deflected shot.

The No. 3 Eagles snapped a two-year drought from reaching the Garden Sunday afternoon, defeating a resilient Vermont team 4-3 in overtime.

“Ladies and gentleman, we were treated to some good hockey,” Vermont coach Kevin Sneddon said. “That was one of the best college hockey games I’ve been involved with in some time.”

The game was a back and forth affair, with neither team more than a goal up the entire game. Both teams traded goals in both periods, setting up a third period where, ultimately, every goal was crucial.

In the third period, the Catamounts struck first.

Conor O’Neil, in the second period, had tied the game for the Catamounts on a goal scored in the slot. The third period yielded another goal for the freshman. On a rebound created by Brady Shaw, who returned Sunday from suspension, O’Neil buried the puck, giving Vermont its first lead of the game. The goal marked the beginning of an onslaught by the Catamounts that moved through the duration of the first half of the period.

But then, the Eagles got some offense from an unlikely source.

Before the game, BC coach Jerry York changed the lines, moving J.D. Dudek onto a line with Colin White and Ryan Fitzgerald.

“I think the way Joey Dudek’s been playing, we just want to give him some more ice time,” York said. “He’s been used very sparingly this year, but he’s starting to play very well.”

Dudek supported the confidence of his coach, redirecting a Casey Fitzgerald shot past Packy Munson, tying the game at three, and sending the 2,537 at Kelley Rink into a frenzy.

In overtime, early in the period, disaster almost struck for the Eagles. On a chaotic play in front of Demko, the puck somehow ended up on the goal line, spinning, before it was cleared out. Even after review, it was determined that the puck had not crossed the line.

“The hard thing is our bench was pretty convinced that it did go over,” Sneddon said. “When [the officials] came out, it was certainly a letdown.”

York noted that there was some discussion on the BC bench over the play, noting that Adam Gilmour believed that the puck had crossed the line.

With Gilmour and the Vermont bench proven wrong, the stage was set for Ryan Fitzgerald to be the hero. Nearing the halfway point of the period, Fitzgerald took a shot from the slot that ultimately sent his team to the Garden for the first time in three years.

“Gilmour kind of just fed it to me — it was one of those shots that you throw on net and say a quick prayer,” Fitzgerald said.

Fitzgerald noted that the shot got deflected “a few times” on the way to the net.

With the win, the Eagles will face Northeastern Friday night at TD Garden at 8 p.m. EDT.