Jaycob Megna scored his first goal for the Sharks (21-19-2), who have lost two straight and four of five (1-3-1). James Reimer allowed four goals on 13 shots and was pulled 12:32 into the first period. Adin Hill made 15 saves in relief.
"It should be a wake-up call," Sharks forward Andrew Cogliano said. "If that game doesn't alarm you in terms of how fast you can be out of position and how fast you can go the other way coming up on the [road} trip we're coming up on, at the end of the day you shouldn't be in the lineup, to be honest with you.
"That's an alarming game in terms of just everything."
Colton put Tampa Bay ahead 1-0 at 3:17 of the first period when his centering pass bounced off the stick of San Jose defenseman Marc-Edouard Vlasic and passed Reimer's glove side.
"I thought we turned it on a little bit toward the end of the game, but from the puck drop we needed to be ready to go, and that was the kind of attitude that we wanted to have tonight," Colton said.
Stamkos scored his 20th goal of the season to make it 2-0 at 7:45 when he completed a tic-tac-toe play set up by Cal Foote.
Mathieu Joseph increased the lead to 3-0 at 11:04 when he scored on the rebound of Stamkos' shot.
"Our first 10, 15 minutes were a disaster," Sharks coach Bob Boughner said. "I think this is the benchmark if you want to play with the big guys. You have to compete, you have to bring your A-game. It starts with showing up."
Corey Perry pushed the lead to 4-0 at 12:32 and chase Reimer.
"I think we gave them a little too much respect. They're a powerhouse of a team," Reimer said. "We were just caught off guard a little bit."
Megna's first goal in 15 games with the Sharks cut it to 4-1 at 16:40.
Brayden Point made it 5-1 at 6:24 of the second period when he was set up by Nikita Kucherov on a 2-on-1.