Logan Couture scored twice in a first period 2, at HP Pavilion.
"It was just one of those nights where the puck was following me around," said Couture. "It felt really good out there and we were able to jump on them quick."
The first goal of the game came 3:26 in when Joe Thornton sent a pass from behind the net to the front and Benn Ferriero got it in on his second attempt.
Just 1:25 later, the Sharks took a 2-0 lead with a power-play goal as Burns' shot from the left circle was stopped, but Joe Pavelski was there to tap home the rebound.
Exactly 90 seconds later, the Sharks made it a 3-0 game on Andrew Desjardins' wraparound from the right side, prompting the goaltending change.
Couture's first goal of the period came at the 13:13 mark of the frame when Marleau made a perfect pass from the right point to the left wing and Couture put the puck in.
Just 1:34 later, Couture scored his 14th goal of the season on the power play for a 5-0 lead.
Moore's goal less than a minute later staunched the bleeding for Tampa Bay.
After a scoreless second period, Burns scored 1:15 in and St. Louis netted his 10th of the year at the 7:45 mark.
Marleau was given credit for a goal that hit several bodies in front after a Couture shot with 7:19 to play to cap the scoring.
It was a season-high in goals for the Sharks...Tampa had given up seven goals in a game two previous times this season...It was the fastest five goals for the Sharks in their team history...San Jose has won six of the last seven against Tampa Bay...The Sharks were 2-for-4 on the power play while Tampa went 0-for-5...Before the game, San Jose announced that forward Marty Havlat will miss the next 6-to-8 weeks after undergoing surgery to repair a partially torn tendon in his left hamstring.