Swayman made 24 saves and stopped all three attempts he faced in the shootout for the Bruins (15-12-0), who had lost four of six, including 6-2 to the New York Rangers on Friday. Elias Lindholm had two assists.

“It’s huge,” Boston coach Marco Sturm said of Swayman’s performance. “You guys feel it, the fans feel it, and more importantly, our players feel it. It’s such a good feeling when you have that. Since Day 1 he’s been rock-solid off the ice and on the ice. The calmness he brings in every game and giving us a chance to win every game is a good feeling.”

Lucas Raymond and Michael Rasmussen scored, and Dylan Larkin had two assists for the Red Wings (13-11-2), who have lost four in a row (0-3-1). Cam Talbot made 17 saves.

The teams will complete a home-and-home series in Detroit on Tuesday.

“It was really important for our team,” Detroit coach Todd McLellan said about earning a point. “It was a tough game to play I think for both teams. There was a lot of checking, not a lot of loose ice, and at times, frustrating for both teams. For us to find our game as the night went on was a real positive sign. A little disappointing with special teams: power play, penalty kill and shootout. We were on the short end of it. You can’t lose all three and we did tonight, so that’s why we gave up a point. We had some good efforts from some players, and we’re going to need more of it.”

Geekie gave the Bruins a 1-0 lead at 4:25 of the second period. Red Wing defenseman Ben Chiarot tried to clear the puck up the right boards, but it went right to Lindholm, who sent a quick one-timer toward the net, where Geekie redirected it short side on Talbot.