The Red Wings (6-3-0), who had won six in a row, did not have a shot on goal in the first 10 minutes.
"They were hungrier than we were all over the ice," Detroit coach Jeff Blashill said.
Rask said Detroit's lack of offense eventually became a problem.
"That wasn't the ideal start for me, because you don't want to go that long without a shot, especially coming off an injury," he said. "The guys did a great job of checking and blocking shots all night."
Boston defenseman Torey Krug took a holding penalty at 7:38 of the third period, but the Bruins held the Red Wings to one low-percentage shot on the power play.
Blashill put together his three fastest skaters in the third period -- Larkin, Darren Helm and Andreas Athanasiou -- and Helm drew a boarding penalty with 1:13 to play. With a 6-on-4 advantage, Detroit got two shots before time expired.
Red Wings captain Henrik Zetterberg said Detroit's power play (0-for-4) was a factor.
"Everything was wrong," he said. "We couldn't get the puck into the zone, we couldn't break out of our end, we didn't win faceoffs, we didn't get pucks on net. I could go on."