Tampa Bay led 3-1 after 20 minutes on a pair of goals from Brayden Point and another from Ross Colton. That would be all the offense the Bolts could muster, however.
The Sharks scored the final two goals of regulation, before Timo Meier delivered the game-winner at 2:19 of the extra session.
For the Lightning, they only manage a single point out of the back-to-back coming out of the All-Star break.
Tampa Bay is back in action on Thursday against the Avalanche at AMALIE Arena.
Scoring Summary
1st Period
TBL 1, SJS 0
2:10 Ross Colton (11) - Zach Bogosian
After getting blown out one night earlier, the Bolts got off to an ideal start on Tuesday, grabbing the lead just over two minutes in. Zach Bogosian pinched at the point to hold play in the zone and fed Ross Colton down low. Kaapo Kahkonen had come out of his crease to try and intercept the pass, but Colton was able to step around the goaltender and score into the wide open net.
TBL 1, SJS 1
6:28 Erik Karlsson (17) - Timo Meier, Tomas Hertl - PPG
It took the Sharks just five seconds into their first power play to tie the game at one. San Jose won the opening draw back to Erik Karlsson, and he wound up a heavy slapshot that beat Brian Elliott for the equalizer.
TBL 2, SJS 1
9:21 Brayden Point (30) - Nikita Kucherov, Victor Hedman - PPG
The Bolts went back in front midway through the period on a Brayden Point power play goal. On the rush, Nikita Kucherov avoided pressure along the far wall and dished to Point inside the left circle. Point snapped his shot upstairs on Kahkonen.
TBL 3, SJS 1
16:44 Brayden Point (31) - Mikhail Sergachev, Nikita Kucherov
Point added his second goal of the opening period seven minutes later. Mikhail Sergachev's initial shot was blocked in front but fell to Point in the slot, and he quickly fired the rebound home.
2nd Period
TBL 3, SJS 2
16:23 Timo Meier (29) - Alex Barabanov, Logan Couture - PPG
Again the Sharks scored right off the opening draw of the power play, this time getting back within one on Timo Meier's goal. There was a tie-up off faceoff, but eventually the puck came free for Alex Barabanov down low to send a cross-crease feed to Meier for the goal.
3rd Period
TBL 3, SJS 3
3:08 Scott Harrington (2) - Erik Karlsson
An inadvertent deflection from Pierre-Edouard Bellemare led to San Jose's first even strength goal of the game. Scott Harrington got credit for the goal, taking a shot from the point that changed direction and beat Elliott because of a redirection off Bellemare's stick.
Overtime
SJS 4, TBL 3
2:19 Timo Meier (30) - Erik Karlsson, Tomas Hertl
Tampa Bay barely touched the puck in overtime and eventually conceded the game-winning goal to Meier. Karlsson played a pass across to Meier at the far post and he tapped it over the line to secure the second point for the Sharks.
