"The power play is based on results and not how many chances you get," Boston defenseman Brian Leetch said. "We missed a chance to get points last night, so it magnified the importance of this game."
Sturm scored when Leetch's shot from the corner deflected off Sturm's skate and through Thrashers goalie Kari Lehtonen's legs.
"To leave this building empty-handed is unbelievable," Thrashers coach Bob Hartley said. "I feel very sorry for my players."
Raycroft made 20 saves for his first win since Jan. 7 and helped the Bruins snap a three-game losing streak.
"There was not as much pressure on me tonight knowing I hadn't played in a while," Raycroft said. "At the same time, if we had lost, we could have been eight points behind three teams."
Atlanta's Ilya Kovalchuk tied it at 2 at 7:19 of the third period when his point-blank wrist shot went over Raycroft's shoulder.
Atlanta lost for the second time in six games and ended a franchise-best three-game road winning streak.
"It was just a lucky bounce and it came so late that we didn't have time to regroup," Lehtonen said.
Tom Fitzgerald put the Bruins ahead 2-1 when he knocked in his own rebound with 11:55 remaining in the second period.
"We played too good of a game to give this one away," Sturm said.
Peter Bondra tied it at 1 with a power-play goal 50 seconds later after the Bruins took three consecutive minor penalties in a 1:28 span.
Bondra scored his third goal in three months for Atlanta.
Fitzgerald has three goals this season, two in the last two games. ... Brad Boyes assisted on the winning goal for Boston. He has seven assists in the last five games. ... Bruins goalie Tim Thomas had his consecutive start streak snapped at 16 games. ... P.J. Axelsson missed the game with a knee injury. Axelsson was honored before the game for winning a gold medal with Sweden... Boston is 4-0-1 in its last five home games against Atlanta. ...
Kovalchuk has 18 points in 14 career games against Boston.