The Black & Gold then found themselves down two goals early in the second period despite carrying play for the vast majority of the opening two frames.
But through it all, Boston managed to battle back behind goals from Charlie Coyle and Curtis Lazar to pull out a well-earned point in a 3-2 overtime loss to two-time defending champion Tampa on Saturday night at TD Garden.
"You want to get every point you can. You work back from a couple of goals to gain one, and that's huge down the road. Of course, we wanted to finish it off. We had some opportunities, and we didn't. [Jeremy Swayman] played some good hockey to keep us in it. And they're a good team," Charlie Coyle said after Lightning captain Steven Stamkos handed Boston its first OT setback of the season with the winning tally at 1:31 of the extra session.
"But you want every point you can. One side of it, I think it's good to claw back and work and grab that point, but there's also some things we can work on when you don't win a game. We can look at that and come back and get better from it."
After falling behind, 2-0, on a shorthanded tally from Taylor Raddysh and a whacky deflection off an Ondrej Palat shot, the Bruins - who outshot Tampa, 39-25, for the game - kept pushing. Coyle pulled Boston within a goal when he finished off a gorgeous behind-the-back feed from Erik Haula with 3:30 left in the second, before Curtis Lazar knotted things at 2 with a beautiful, backhanded finish at 4:44 of the third.
"I think our guys played real well tonight, especially being down 2-0 to that team," said Bruins assistant coach Joe Sacco. "But, even when we were down, 2-0, we were playing a good, solid game, and I thought the process was good for our guys. And we felt that being down, 2-0, we were still in the game.
"When we got that goal there in the second period, that kind of lifted us again and got us right back in there. We played hard tonight. We competed. Really nobody took the night off. We had everybody on board, and it was good to see. Unfortunately, we don't get the end result, the extra point, but we can build off that game, for sure."