They were outplayed early in the game badly but managed to tie, then lost when David Pastrnak scored with 46.9 seconds left in overtime, giving the Bruins a 4-3 victory.
It was the Red Wings' (20-19-9, 49 points) third consecutive overtime loss.
Boston put 47 shots on goalie Jared Coreau through regulation time but Coreau was superb throughout the evening, and was the sole reason the Red Wings were able to steal a point.
Boston's Brad Marchand tied it 3-3 with his second goal of the game at 8:20 of the third period.
The Bruins came on a rush, put together a nice passing play, and Marchand poked in his 19th goal past Coreau.
Mike Green and Tomas Tatar scored second period goals, giving the Red Wings a 3-2 lead after 40 minutes they probably didn't deserve.
Andreas Athanasiou scored a breakaway goal in the first period.
The Red Wings were completely out-played in the opening 20 minutes, Boston outshooting the Red Wings 21-7 (10-0 through 10 minutes).
But Green tied the game at 2 with his ninth goal at 6:25.
Green had the puck on the point and lifted a shot toward net that bounced off the skate of Bruins defenseman Kevan Miller and got past Rask.
Coreau had to withstand another Bruins flurry shortly after, and the Red Wings capitalized.
Henrik Zetterberg found Tatar skating down the wing, with the Boston defense allowing Tatar plenty of space and time.
Tatar skated down to the low circle and snapped a wrist shot through Rask's legs, the puck tricking into the net for Tatar's 11th goal at 10:51.
Athanasiou provided the lone offense in the first period with another highlight reel breakaway goal.
Trailing 1-0, Green found Athanasiou behind the Boston defense.
Athanasiou sped through the defensive tandem of Zdeno Chara and Brandon Carlo, went in alone on Rask, and scored his 11th goal, sixth in the last 10 games.
Other than Athanasiou's goal, it was another brutal first period for the Red Wings, matching a similar wretched opening 20 minutes from a week ago.
Coreau was called upon often to bail the Red Wings out- and he did.
Kevan Miller made it 1-0 for the Bruins with a shot from the edge of the circle, his first goal, at 3:39. Coreau was screened and didn't appear to get a clear look on the shot.
Athanasiou tied it at 1, but the Bruins regained the lead on the power play.
With Jonathan Ericsson in the box for playing with a broken stick, Boston's Brad Marchand put back a rebound that Coreau couldn't control at 17:34, Marchand's 18th goal.
Tuesday's game marked the opening of back-to-back games to close out the schedule before this weekend's All-Star break against Boston and Toronto – two teams ahead of the Red Wings in the Atlantic Division.
With the standings to close and bunched together, any points gained on teams ahead of the Red Wings are vital.
"They're big games, division games against teams that we're chasing," Zetterberg said. "We know going down the stretch there's going to be a lot of these games, which is a good thing for us. If we win these games, we're gaining ground."
Said coach Jeff Blashill: "There's no question there are teams we're trying to jump and in order to jump teams, you have to beat them at some point, so we have to find a way to do that."