The victory, four days after a 5-3 win in Buffalo, gave the Penguins a three-point lead in the race for the No. 4 seed in the Eastern Conference -- and home advantage in the first round -- over the Philadelphia Flyers, who lost to the New York Rangers 5-3.
Pittsburgh's hope of finishing first in the conference was lost when the Rangers won.
The Bruins, who clinched the Northeast Division title on Sunday night, are 7-2-1 in their last 10 games.
The Penguins and Flyers have two games left and will face each other in Pittsburgh in the regular-season finale on Saturday.
"Toward the end, I'm sure guys were taking a peek a little more at the out-of-town scoreboard," Crosby said, "but I think, for the most part, we've got to worry about ourselves and getting points."
In Pittsburgh's first game since a late brawl Sunday against the Flyers, Crosby gave the Penguins a 1-0 lead 7:41 in. He made it 4-2 with 1:11 left in the second period with his club's second power-play goal in 48 seconds.
"It was a pretty emotional game" against the Flyers, the Penguins' likely first-round opponent, Crosby said. "So any time you play one like that you've got to really bear down and find a way to get up for the next one."
"I thought we played a pretty decent game, and we had lots of chances, certainly didn't bury enough," Bruins coach Claude Julien said, "but I'm not disappointed in our game."
Earlier Tuesday, hockey analyst Mike Milbury apologized for critical comments he made about Crosby. On a Philadelphia radio station on Monday, Milbury called Crosby "a punk" and criticized his role in the lead-up to the brawl with just over a minute left in Philadelphia's 6-4 win.
The fighting resulted in 52 penalty minutes and began, in part, with Flyers forward Brayden Schenn's cross-check to Crosby.
"I don't know what he's looking for, if he's looking for attention. I don't know what it is," Crosby said of Milbury before Tuesday's game. "I really don't know where that came from. He's pretty good at twisting things around, that's for sure."
Against the Bruins, Crosby went back to doing what he does best -- sparking the Penguins' offense. He has five goals and 17 assists in 12 games since returning from concussion-like symptoms that have limited him to 20 games this season.
His first goal came when he flipped the puck over goalie Marty Turco from the left side after taking a pass from Pascal Dupuis with each team having a player in the penalty box.
"Both goals were great passes by other people, but also the finish is there," Turco said.
Martin made it 2-0 at 14:58 of the period. He shot the puck from the left and kept skating in as Turco saved it. As he was being dragged down by Johnny Boychuk, the puck deflected off Martin's glove and into the net for his second goal of the season. The goal was upheld after a video review.
Pouliot cut the lead in half two minutes later with his 15th goal of the season on a backhander from low in the right circle. Lucic tied it 18 seconds into the second period with his 25th goal. David Krejci collected a rebound just in front of the crease, and backhanded the puck to Lucic, who fired it quickly past goalie Brent Johnson.
But when Daniel Paille was called for charging at 17:20, and Peverley followed him into the penalty box on a high-sticking call 9 seconds later, the Penguins had a two-man advantage.
It took them just 42 seconds to break the tie on Neal's 40th goal. Crosby, standing on the goal line to the left of the net, passed into the crease where it went by Penguins forward Chris Kunitz. But Neal was right behind him to score from 10 feet.
"It's been a lot of fun," Neal said. "We did a good job coming in here and playing a tough Bruins team and fighting for that home-ice advantage."
Less than a minute later, Crosby scored his seventh of the season from the lower left circle after Kris Letang sent him a pass from the right side.
"We have to show character in not quitting until the last minute," Bruins forward Tyler Seguin said. "Even though we were down two goals, we were down 2-0 and came back and made it 2-2."
Asham made it 5-2 at 6:15 of the third, and Peverley scored two minutes later.
Boychuk and Penguins center Joe Vitale were helped off the ice with injuries in the third period. Julien said Boychuk was hit on the side of the leg and would be re-evaluated on Wednesday. Pittsburgh coach Dan Bylsma didn't provide an update on Vitale. ... Dupuis recorded a point in his 15th straight game, the longest streak in the NHL this season. He has nine goals and 11 assists in that span. ... Having clinched the division title, the Bruins rested No. 1 goalie Tim Thomas. ... Bruins defenseman Torey Krug made his NHL debut. The Bruins signed him on March 25 as a free agent from Michigan State.
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BOSTON, MA - APRIL 03: Sidney Crosby #87 of the Pittsburgh Penguins is congratulated by teammates Jordan Staal...