Marcel Goc, Ryane Clowe and Devin Setoguchi scored for the Sharks, who have opened the season by winning seven of nine.
Tampa Bay goalie Mike Smith stopped 42 shots. The Lightning, under new coach Barry Melrose, are 1-3-3.
Boucher turned aside 21 shots in his first game of the season in San Jose's 1-0 win over the Los Angles Kings 1-0 on Oct. 12.
Goc stopped a 22-game goal-scoring drought to put San Jose up 1-0 from the top of the left circle at 7:57 of the second. Former Lightning defenseman Dan Boyle, playing in Tampa for the first time since an offseason trade to San Jose, had the assist.
The Lightning nearly tied it later in the second, but Martin St. Louis' shot during a power play hit the crossbar. Boucher also made a nice save on a slot shot by Vinny Prospal.
Clowe made it 2-0 on a power-play goal with 2 minutes left in the second when he redirected Christian Ehrhoff's blue-line shot. Setoguchi gave the Sharks a 3-0 lead with 3:32 remaining in the third.
Smith stopped 16 shots in a scoreless first, including a sliding save on an in-close rebound by Milan Michalek late in the period. The Lightning got nine shots, including two by 2008 first overall draft pick Steven Stamkos over the stretch.
Stamkos is still looking for his first NHL point after playing in seven games.
Notes:@ San Jose C Joe Thornton, bothered by a sore groin muscle, had an assist. ... Lightning RW Radim Vrbata (groin) didn't play. ...Tampa Bay D Marek Malik, signed to a one-year contract Thursday, made his Tampa Bay debut. ... Goc's goal was his first since Feb. 18 against the New York Islanders. ... Former Lightning GM Jay Feaster was at the game.