Tampa Bay went 2-1-0 on a three-game California road trip.
"I take this as a success," Lightning coach Jon Cooper said. "It's been a tough start with all these road games we've played, so let's go home and see if you can string a few [wins] together."
Erik Karlsson scored twice for the Sharks (3-8-0), who have lost two of three. James Reimer made 22 saves.
"We weren't afraid of losing today," Karlsson said. "We did, and it hurts. And we're disappointed. I think one of the problems here lately has been that we've been a little bit too afraid to make mistakes, and a little bit too afraid to try and win games. And in order to win games in this league, you're gonna have to take some risks. Over time, we're going to [have to] learn when those risks are appropriate to take and when they're not."
Victor Hedman scored 32 seconds into the first period off a set-up by Point to give Tampa Bay a 1-0 lead.
Karlsson tied it 1-1 at 1:22 with a wrist shot from between the face-off circles.
"He's a very special player," Sharks defenseman Mario Ferraro said of Karlsson. "He's very important for our team. He's a leader, especially in the way he plays, and that's what we need. We expect nothing less."
Ross Colton put the Lightning back in front 2-1 at 13:44, scoring with a wrist shot just as the Lightning's first power play of the game expired.
Nico Sturm tied it back up 2-2 at 5:36 of the second period.