Garnet Hathaway fends off a check by Detroit’s Dylan Larkin and steers the puck past Red Wings goaltender Magnus Hellberg for Boston’s winning goal Saturday at TD Garden. Mary Schwalm/Associated Press

BOSTON — The Boston Bruins’ T-shirt factory is struggling to keep up with all the milestones the team is cruising past on its way to the Presidents’ Trophy.

“Fifty wins, it’s amazing,” said forward A.J. Greer, who was wearing a shirt commemorating Patrice Bergeron’s 1,000th NHL point while discussing Boston’s 50th win of the season, a 3-2 victory over Detroit 3-2 on Saturday.

The Bruins are the fastest team to 50 wins in NHL history.

“I love playing for this team,” Greer said after assisting on Garnet Hathaway’s winner with six minutes left. “I love wearing the Bruins logo, and especially with the results, it’s been an amazing journey so far. But we’re not really focused on anything right now besides playing the right way for 60 minutes every night.”

Hathaway, a Kennebunkport native, gathered in a rebound and poked it in to break a third-period tie as Boston rallied from a two-goal deficit and improved to 50-9-5. The 50 wins in 64 games broke the record of 66 games set by the 1995-96 Red Wings and matched by the 2018-19 Lightning.

“Congrats to us then, I guess,” said goalie Linus Ullmark, who stopped 30 shots. “But we focus on the process, and our process is what’s important.”

The Bruins, who already were the fastest ever to 100 points, could become the first team this season to clinch a playoff berth if the Islanders beat the Capitals or the Canucks beat the Senators in regulation later Saturday.

“Fifty wins is great. And it’s kind of a testament to how hard this team has continued to work throughout the year,” Hathaway said before the team headed to Detroit for a rematch with the Red Wings on Sunday. “But I think guys want 51, you know? Guys are excited to play this team tomorrow already.”

After blowing a two-goal lead and losing 3-2 to Edmonton on Thursday night, snapping a 10-game winning streak, the Bruins fell behind 2-0 on Saturday before the game was 5 minutes old. But Hampus Lindholm and Bergeron scored 88 seconds apart in the second period, when Boston had an 18-2 edge in shots, including the first 12.

Hathaway broke the tie in the third as the Bruins avoided back-to-back losses at home.

“We never want to lose two in a row. We showed that today,” Ullmark said. “We came out a little slow. They came out hot as well. Give them credit, they really came here to play in that first period and we were just weren’t ready for it.

“But we took a breather in between the first and second, and we told each other we’ve got to ramp it up a little bit. And then we absolutely dominated them in the second.”

Magnus Hellberg made 35 saves for Detroit, which snapped a six-game losing streak by beating Chicago on Thursday. Andrew Copp scored a short-handed goal in the second minute of the first period, and Alex Chiasson also scored, giving the Red Wings a 2-0 lead just 4:32 in.

Lindholm scored at 12:43 of the second. The Red Wings appeared to respond quickly, but a Dylan Larkin’s goal was taken off the board because he smacked the stick out of David Krejci’s hands seconds earlier, drawing an interference penalty.

Instead, Bergeron tied it on the ensuing power play, deflecting a pass from Jake DeBrusk through Hellberg’s legs. It stayed that way until Hathaway tallied his 10th of the season and his first since arriving in Boston before the trade deadline from the Washington Capitals.