BOSTON — Ryan O’Reilly scored for the fourth straight game and rookie Jordan Binnington stopped 32 shots in Game 7 of the Stanley Cup Final on Wednesday night to lead the St. Louis Blues to a 4-1 victory over the Boston Bruins and their first NHL championship in the team’s 51-year history.

Alex Pietrangelo added a goal and an assist and Brayden Schenn and Zach Sanford also scored for St. Louis. The Blues woke up on New Year’s morning with the worst record in the league but won 30 of their final 49 regular-season games and soared through the playoffs to reach the final for the first time since 1970.

Coach Craig Berube, who took over when Mike Yeo was fired in November, is the fourth coach in the past 11 years hired in midseason to lead his team to the NHL title.

O’Reilly was named the Conn Smythe Trophy winner as the most valuable player of the playoffs.

O’Reilly set a Blues record with 23 playoff points, became the first player since Wayne Gretzky in 1985 to score in four consecutive Cup Final games and did it all with his grandmother on his mind.

“She’s one of my biggest supporters,” O’Reilly said before the game. “I’m hoping I could bring the Cup to her.”

O’Reilly’s grandmother watches and emails him from Seaforth, Ontario, where he grew up playing hockey. She bought him multiple pairs of skates when he was a kid and has tracked his progress very closely.

“She’s obviously a big part of my career,” O’Reilly said.

After scoring just three goals in his first 22 playoff games, O’Reilly scored five in the past four to carry the Blues to the Stanley Cup.

Matt Grzelcyk scored the Bruins’ only goal, and Tuukka Rask stopped 16 shots for Boston.

Boston outshot St. Louis 33-20, but the Blues went ahead at the end of the first period on goals from Reilly and Pietrangelo about three minutes apart. The second period was scoreless, then Schenn put it out of reach with 8:35 to play and Sanford made it 4-0 before the Bruins spoiled Binnington’s bid for a shutout.

Returning to the site of their last appearance in the final, which ended when Bobby Orr sailed through the air after scoring the Cup winner, the Blues won for the third time in Boston this series and an NHL record-tying 10th time in the postseason.

The Blues had just one shot on goal heading into the final minutes of the first period, but they scored first when O’Reilly deflected a shot from Jay Bouwmeester into the net. Then with just 8 seconds left in the period and Bruins forward Brad Marchand tentative on a line change, Pietrangelo beat Rask to make it 2-0.

Bouwmeester played in 1,184 regular-season games — the third most among active players who had not gotten their names etched on the Stanley Cup.

St. Louis showed it could put a stranglehold on opponents when playing with a lead. The Blues finished the playoffs 13-4 when scoring first, 8-2 when leading after one period and 10-1 when leading after two.

Bruins coach Bruce Cassidy conceded that the Blues “play a different game” when they’re ahead.

Because of how well the Blues defend and even move the puck differently when they’re ahead in a game, it gets increasingly difficult for an opponent to come back on the Blues. They also went 4-1 in chances to eliminate a team — and after losing Game 6 on home ice were clinical in holding on to a multigoal lead in Game 7.

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