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BOSTON — It now is 51 years and counting, but the Blues still haven’t won a game in the Stanley Cup Final.

They were swept in four games in their three previous Cup Final appearances — in 1968 and 1969 against the Montreal Canadiens and in 1970 against the Boston Bruins.

On Monday night it was same story, different century.

The Blues looked good early, jumping to a 2-0 lead early in the second period. But with towel-waving Robert Kraft, owner of football’s New England Patriots in the house, Boston stormed back for a 4-2 victory at TD Garden in Game 1 of the best-of-seven series.

It was the Bruins’ eighth straight victory in these playoffs — they have outscored their opponents 32-11 in that stretch. And it ran their postseason record to 9-0 against the Blues, including a 4-0 sweep in the 1970 Stanley Cup Final, they last time the Blues were in the title round.

“We’ve been real disciplined most of the playoffs pretty much,” coach Craig Berube said. “We weren’t tonight obviously with five penalties. We gotta be better there.”

Entering Monday’s contest, the Blues were the least penalized team in the playoffs this season, spending an average of 6.18 minutes in the penalty box per game. That wasn’t the case Monday, when they were whistled for five penalties compared to two for Boston.

“I’m not gonna judge the calls, but they did happen,” Perron said. “We were in the box too much and that gave them the chance to get their touches and kinda get going in their game and shoot pucks on net.

“The number (of shots) looked bad and a lot of it happened on the power play. And we just didn’t play good enough in the second.”

No they didn’t. After taking a 2-0 lead one minute into the second period on Vladimir Tarasenko’s ninth goal of the playoffs, it was all Boston.

Connor Clifton got behind the Blues’ defense for a tap-in goal on a pinpoint pass from Sean Kuraly 76 seconds after Tarasenko’s goal. Clifton beat his former teammate from the Providence Bruins, goalie Jordan Binnington, on the play.

Charlie McAvoy scored on the power play with 7:19 left in the period to tie the game at 2-2. And then Kuraly got the winner 5:21 into the third period getting the puck past Joel Edmundson and then Binnington during a scramble in front of the net.

The Blues were outshot 18-3 in the second period and 30-12 over the final two periods.

“It’s just a reflection of we didn’t have the puck down low,” the Blues’ Jay Bouwmeester said. “We just played into their hands. It’s tough to win when you take five penalties, especially against a team that has a real good power play.”

It took several scrambling saves and spectacular saves by Binnington to keep the Blues in it before Brad Marchand scored an empty-net goal with 1:49 left.

“When that first goal went in they got some momentum, and then a big push there,” said Binnington, who made 34 saves. “You could feel them coming and they were coming hard and the rink was buzzing.”

In comparison, the Blues mustered only 20 shots and went the last 11:44 of the second and the first 4:33 of the third without a shot on goal — a total drought of 16:17.

“I think we’re fine in here,” Perron said. “We know what we did is we went to the box too much. We lost our composure a little bit. We were not getting to our game enough below the goal line, things like that.

But I think we’re gonna be a lot better next game.”

The Bruins entered the game with a scalding 34 percent success rate on the power play in the postseason, so the Blues were playing into their hands by sending out the Boston power play so many times. And the Blues weren’t always happy about the calls.

Edmundson was sent off for high-sticking former Blues captain David Backes 5½ minutes into the second period.

Edmundson reacted as if he thought Backes was guilty of embellishment, and gave a shove to Backes in the back while the Boston forward was on the ice.

The Blues killed that one off. They weren’t as fortunate 5½ minutes later when Oskar Sundqvist was sent off for hooking, at the 11:04 mark of the second. Sundqvist complained about that call as well, drawing boos from the crowd at TD Garden. That penalty led to the game-tying goal by McAvoy.

“Yeah, I mean there’s a couple where we weren’t sure,” Perron said. “But it is what it is. . . . It’s a fast game out there and we just gotta make sure our sticks aren’t in there. Same with my penalty.”

This is Boston’s 20th Stanley Cup Final and Monday marked its first victory in those 20 when trailing by two or more goals.

But it was more than the penalties that stymied St. Louis. The Blues just couldn’t generate anything for most of the final two periods, as a quick, aggressive Boston squad kept the Blues bottled up in their own zone much of the time.

“They pressure you. They come hard,” Berube said. “They’re a quick team. They get on you. They’ve got good sticks. They do a lot of good things. . . . They force you into bad situations with the puck a lot of times.”

And in terms of physical play, they matched the Blues hit by hit. By game’s end Boston had 32 hits to the Blues’ 33. A hit by Torey Krug leveled Robert Thomas midway through the third period and the Blues’ rookie did not return.