Thomas made a season-high 45 saves to lead Boston to a 4-1 victory on Tuesday night.
Thomas was solid in that one and steady throughout on Tuesday, when Boston won despite being outshot 46-24.
"We're fighting to get back into the race," said Thomas, whose team entered the weekend last in the Northeast Division. "We had a meeting this morning and Coach said this was the closet thing we've had to a playoff game. To get to the playoffs we have to beat teams like the Maple Leafs. He basically challenged us."
Murray scored the game-winner at 5:35 of the third, Sturm added an insurance goal at 17:07 and Boyes scored an empty-netter at 19:36.
The Bruins entered the series 10 points behind second-place Toronto -- but now trail the Maple Leafs by six.
"We're trying to climb the standings," Murray said. "Every win is huge for us. We got behind the 8-ball early in the season."
Thomas credited his defense for clearing rebounds and allowing him to see the shots.
"The Leafs wanted to redeem themselves so they were throwing everything at the net," he said.
Top defenseman Bryan McCabe left in the third period with a sprained left ankle, but is not expected to be out for long.
"We had a much better night than Saturday night, but we've got to put the puck in the net on power-play opportunities," said Toronto coach Paul Maurice, whose team went 0-for-6 with the man advantage.
Former Bruins goalie Andrew Raycroft lost his second straight game to Boston. He was traded to Toronto after struggling in Boston last season.
Boston's Petr Tenkrat skated past the blue line before passing to Murray, whose slap shot beat Raycroft glove side.
"I've seen him a little bit the past few years. I know his tendencies," Murray said with a smile.
Donovan skated in on a 2-on-1 before beating Raycroft with a wrist shot glove side at 3:59 of the second.
After Toronto's Michael Peca put a shot on goal, Antropov put the rebound past Thomas. The officials waived the goal off after it looked as though Antropov kicked it in. But after the play was reviewed, the goal was awarded to Toronto at 15:39 of the second.
The Maple Leafs had a two-man advantage early in the third, but Darcy Tucker missed the net on a one-timer and Toronto didn't put many shots on net.
Toronto went on the power play again late in the period, but failed to capitalize.
- Toronto defenseman Pavel Kubina changed his number from 73 to 31. Kubina took a puck to the face in Saturday's loss and has played in just 10 games this season because of injuries. He has no goals and just two assists. Toronto signed him to a four-year, $20 million contract in the offseason.
- The Maple Leafs traded third-string goalie Mikael Tellqvist to Phoenix. Toronto received forward Tyson Nash and a fourth-round draft pick in 2007.