Crosby tied the game 3-3 with his NHL-leading 20th goal of the season at 5:08 of the third period. Kessel made the pass, and Crosby scored on a one-timer from between the circles.
"We definitely executed really well, especially late in the second with a quick one to get it close," Crosby said. "We had some really good looks."
Filppula gave the Lightning a 2-1 lead at 3:38 of the second period when he beat Matt Murray with a wrist shot to the near post on a 2-on-1. Drouin made it 3-1 at 10:19 of the second on a partial breakaway.
"I thought we played well, it definitely [stinks] to lose that one," Drouin said. "We were physically and mentally going and the bench was going and I hadn't seen [that] in a while from our team, so it was a nice to see."
Crosby made it 1-0 at 12:03 of the first period, and Drouin tied the game 1-1 with a power-play goal at 17:57.
Crosby left the game briefly in the first period when he was checked by Lightning defenseman Luke Witkowski and his head hit the boards where they meet the glass. Crosby said he had to go through the concussion protocol at the end of the first period.
"It was just kind of a stinger," Crosby said. "My neck got jammed and that's basically it."