Boston University bench boss Jack Parker has said the Beanpot would benefit from some fresh blood in the winner’s circle to break the icy ennui. It’s hard to argue with Parker’s preference for a little more puck parity, except when BU and BC play a Beanpot final like last night.

What other matchup would you have wanted in the Beanpot final? If you can’t enjoy the Commonwealth Avenue adversaries and their legendary coaches, Parker and BC’s Jerry York, duking it out as they did on the TD Garden ice, then you don’t have a pulse.

The Terriers were seeking their fifth Beanpot title in six seasons and 30th overall, but BC held on for a 4-3 victory and its second Beanpot title in three years and 15th overall. But the real winners were college hockey fans.

“If there was a classic Beanpot that would be one of them,’’ said York, who won his fourth Beanpot with BC. “I’ve been involved in a lot of really good matchups here, but this particular one was quick, it was fast. Even at 4-1, none of us thought the game was finished yet, and BU put on a terrific surge there at the end with a shorthanded goal and then the six-on-four goal to make it a game that’s in doubt right until the final buzzer.’’

The game was in doubt right up until BC goalie and Beanpot MVP John Muse (a dead-ringer for Red Sox pitcher Jon Lester) snuffed out BU’s Nick Bonino on the doorstep with 19.8 seconds left. Bonino lifts the puck a few inches and we have overtime.

Let’s just say Bonino wasn’t the only one robbed by Muse, who stopped 31 shots. With all due re spect to Parker and the fine schools of Northeastern and Harvard, it’s hard to get enough of the BC-BU rivalry.

Parker had opined that maybe it would be better for the tournament if BU or BC didn’t win it, something that hasn’t happened since 1993, when Harvard captured the title. The Green Line-linked institutions of higher learning and hockey have now won the last 17 Beanpots and every one contested at the FleetCenter/TD Banknorth Garden/TD Garden, which became the tournament’s host in 1996.

After last night’s classic, it seemed like even Parker was ready to concede that BC-BU isn’t so bad for the Beanpot.

“I thought it was a great college hockey game,’’ said Parker. “Typical of the games we’ve played so far with this team - closely contested, real emotional. . . . In general it was a real good effort. It’s a game of mistakes. We made a couple. They made a couple. But we certainly put on a pretty good show for the Garden faithful.’’

BU-BC is like Red Sox-Yankees, Duke-UNC, and Celtics-Lakers put on ice, a timeless rivalry that instantly ups the intensity level no matter the stakes.

Last night was the 250th meeting between the ancient enemies and it was a lot like the other 249 - exciting, emotional, and played with an edge. It didn’t take long for the teams to tangle - literally. BC’s Steven Whitney mixed it up with BU’s Zach Cohen behind the Eagles’ net and was whistled for a penalty you normally only hear about in football. At 7:20 of the first, Whitney got two minutes - and a 15-yard penalty - for grabbing the facemask.

Late in the game, it was 5-foot 8-inch, 165-pound BC forward Brian Gibbons who decked 6-foot-4, 219-pound BU defenseman Eric Gryba. That had Parker apoplectic on the BU bench, and he banned his players from talking about the officiating after the game.

The Eagles scored four unanswered goals to take a 4-1 lead at 15:48 of the third period, but then had to withstand a furious Terriers rally that was reminiscent of their Miracle against Miami last year in the NCAA title game to tie the season series between the teams at 2-2.

BU took a 1-0 lead at 13:37 of the first period when BC defenseman Philip Samuelsson, son of Ulf, tried a backhanded pass from behind his own net. It was picked off by Kevin Shattenkirk, who walked in and snapped a shot past Muse.

However, BC scored three second-period goals, the last of which was an ESPN-worthy tally by Boxford’s Chris Kreider. The freshman forward faked Terriers defenseman Max Nicastro out of his skates, then deftly dipped around BU goalie Kieran Millan to tuck a backhander home.

BC propped its lead up to 4-1 at 4:22 of the third. But the Cardiac Canines wouldn’t let the Beanpot go that easily. David Warsofsky netted a shorthanded tally midway through the third, and Parker then pulled Millan for an extra attacker, allowing Mr. Clutch, Colby Cohen, to cut the lead to one with 2:46 left.

If Parker wants to better the Beanpot, how about doing away with the outdated consolation game? It looked like neither Northeastern nor Harvard wanted to be there last night, and the fans certainly didn’t.

“It’s obviously a little hard to pump yourself up,’’ said Harvard’s Conor Morrison, who had the lone Crimson goal in a 4-1 loss. “Neither of these two teams want to be in that situation. We obviously want to be playing in [the championship game], but it’s a big game for both teams because we play each other next year. It’s a good preview.’’

Very diplomatic, Mr. Morrison, but I’m not buying it. However, Morrison was one future Harvard alum who wasn’t put off by the BU-BC final.

“I think I’ll stick around,’’ he said. “I like watching hockey and it should be a great atmosphere.’’

He was right. It was.