Jonathan Quick made 34 saves in his second start with the Golden Knights (2-0-0) after being acquired in a trade from the Columbus Blue Jackets on March 3.
"It's a hockey game," Quick said. "It's that time of the year where every point is huge. It's a great team over there, and we battled hard for those two points."
Point (two goals, one assist) and Kucherov (one goal, two assists) each had three points for the Lightning (38-21-6), who are 1-4-2 in their past seven games and trail the Toronto Maple Leafs by four points for second place in the Atlantic Division. Vasilevskiy made 17 saves.
"I liked everything about the game," Tampa Bay coach Jon Cooper said. "We deserved points tonight. You look at that little slide we had, this is a completely different team. I thought we were way better tonight than we were against Philadelphia (a 5-2 win on Tuesday). This is the best we've played in a while."
Kucherov cut it to 3-2 at 17:53 with a one-timer from beyond the right face-off circle that went off the near post after Vasilevskiy was pulled for an extra attacker.
Point tied it 3-3 on a power play with 28 seconds left after Kucherov faked a one-timer and passed to Point, who scored from the slot.
"It's tough [giving up a lead]," Karlsson said. "You want the two points, but you can't really worry too much about it. You have to focus on the next shift, and that's what we did. So, I think we answered pretty well."