“I think we could even be better, but we were progressing the right way,” Killorn said.
Erik Karlsson scored twice for San Jose, Nico Sturm added a goal and James Reimer made 22 saves.
“I feel a lot better about our team and the direction we’re going in than I did a week ago,” Sharks coach David Quinn said.
A costly mistake leading to the odd-man rush for the winner was something of focus inside the Sharks’ locker room.
“In order to win games in this league, you’re going to have to take some risks,” Karlsson said.
Hedman opened the scoring 32 seconds into the game, and Karlsson tied it 50 seconds later on a blast from the point.
Colton gave Tampa Bay a 2-1 lead with 6:16 left in the first period. Sturm tied it with his fifth of the season at 5:36 of the second, and Killorn put the Lightning back in front with 1:19 left in the second.
“It’s been nice just to get some chemistry going,” Colton said.