The Bruins played without forward Brad Marchand, who served the first of a two-game suspension for spearing Lightning defenseman Jake Dotchin on Tuesday, and lost defenseman Torey Krug to a lower-body injury in the first period.
"They do a great job of shutting the neutral zone down," Bruins defenseman Kevan Miller said. "I think in the first period we did a pretty good job of getting through that. Second and third, they had five guys by the puck the whole game, so tough to get through. I think we did a pretty good job, we deserved better, but it's a tough one."
Stafford scored on a wraparound on the power play at 10:37 of the first period to give the Bruins a 1-0 lead.
Burrows tied it 1-1 at 7:37 of the second period.
"I thought it was a big goal for sure," said Burrows, who has six goals in 18 games since being acquired in a trade from the Vancouver Canucks on Feb. 27. "I thought we were coming better in the second period. We played better and then after that I thought we really played well, we carried the play and we limited their chances. It's nice to get the result that we're looking for, facing adversity lately with injuries. And now it's nice to get in and know that we're going to be playing next week."