Logan Couture had a goal and an assist for the Sharks (22-20-4), who are 1-3-2 in their past six games. James Reimer made 29 saves.
"We've grinded and worked for each other and with each other," San Jose defenseman Brent Burns said. "Just tough. … Close to getting two points a couple of games here. We've been keeping games pretty tight. We need two points though, so it's always frustrating."
San Jose lost to Tampa Bay 7-1 on Jan. 22.
"We talked about the last game and how we weren't happy with the way we played," Sharks coach Bob Boughner said. "I thought we did a good job at the beginning of the game establishing our pace, playing smart, being above them and generating a few chances ourselves."
Cirelli gave the Lightning a 1-0 lead at 1:32 of the second period when he tapped the puck into an open net off a return pass from Brayden Point, who faked a shot and got Reimer to commit.
"It's nice going into the (All-Star) break with a win and playing the game that we did," Cirelli said. "It was a tight checking game, and we weren't turning the pucks over and we protected the middle of the ice. … Doing the little things right."