Point put the Lightning back in front 2-1 at 9:21, taking a back pass from Kucherov and shooting high blocker side from the top of the left circle.
Point then extended the lead to 3-1 at 16:44. He scored past Kahkonen's outstretched left pad in the slot after Mikhail Sergachev's backdoor pass deflected to him off the skate of Marc-Edouard Vlasic.
"I liked our game in the first, and we kind of got away from it in the second," Lightning defenseman Victor Hedman said. "This one stings."
Meier cut it to 3-2 at 16:23 of the second period with a power-play goal. He one-timed a pass from Alexander Barabanov in front shortly following a scramble during a face-off.
"For the first 30 minutes we looked a little rusty, but we found a way to battle back and played real determined," Meier said. "We found a way to get the two points and it feels good."
San Jose finished the game 2-for-3 on the power play. Tampa Bay was 1-for-6.
"I thought we came out and dictated play and did what we wanted to do for 20 minutes," Lightning coach Jon Cooper said. "Then special teams took over, and we lost the special teams game."
Jonah Gadjovich tied it 3-3 at 3:08 of the third period when Scott Harrington's point shot deflected off him in front.
"It feels good to come back and tie the game, get the point and finish it off in overtime," Harrington said. "We've had some poor luck in overtime in the past, so winning the first game after the break feels great. We want to build off this feeling."