TAMPA, Fla. -- Even down two goals late in the second period, Tampa Bay Lightning coach Jon Cooper was confident that his team could cool off Alex Ovechkin and the high-scoring Washington Capitals and rally at least to force overtime.

Tampa Bay did that and more, beating the Capitals 4-3 on Brayden Point's power-play goal at 3:08 of overtime on Monday night at Amalie Arena.

"That was by far the best game we've played," Cooper said, including seven preseason games. "We have a long way to go with this team. ... There were so many positives to take out of this game, but it's game three. It's getting that consistency every single night. Hopefully this is the start."

Ovechkin had hat tricks in each of Washington's first two games, but he was held without a point Monday.

Point scored his third goal of the season in the final seconds of a power play, redirecting a shot by Nikita Kucherov. Washington was called for having too many men on the ice, setting up a four-on-three power play for the Lightning.

"A couple bad penalties there -- we didn't do a great job of playing good 200-foot hockey," said Capitals forward T.J. Oshie, who had two power-play goals as Washington built a 3-1 lead in the second period. "Once we got the lead, it's almost like we sat back and played a little too passive."

Tampa Bay dominated the third period, scoring the tying goal and outshooting the Capitals 17-6.

Kucherov scored into the top right corner of the goal on an assist from Alex Killorn with 9:14 left in regulation to tie it at 3-3.

The Lightning had climbed back within a goal when newcomer Chris Kunitz scored his first goal since joining Tampa Bay, making it a 3-2 game with 1:51 remaining in the second period.

The Capitals came in hot, thanks to seven goals in the first two games from Ovechkin, with assists on all seven from Evgeny Kuznetsov in wins against the Ottawa Senators and Montreal Canadiens.

Washington went with backup goalie Philipp Grubauer on Monday, while Tampa Bay gave starter Andrei Vasilevskiy his third start in four days to open the season. Grubauer made 36 saves, while Vasilevskiy stopped 23 shots.

"Gruby held them off as long as he could there," Oshie said of Grubauer's 16 saves in the third period. "He had a great night."

The Capitals jumped out to a 2-0 lead with a pair of goals in a span of 83 seconds late in the opening period. Nicklas Backstrom got his first goal of the season with 3:18 left, and Washington drew a power play just 21 seconds later on a slashing call.

Oshie followed with the first of his two power-play goals, redirecting a long shot from defenseman John Carlson past Vasilevskiy for a 2-0 lead with 1:55 left in the first.

Tampa Bay answered in the second, with Killorn getting his first goal of the season on an assist from Point with 14:32 left. That pulled the Lightning within 2-1, but a penalty for delay of game on a faceoff set up another power play and another Oshie goal, this one with 12:11 left in the middle period.

"The way this game was going, I liked the way we were playing," Cooper said. "The boys needed to get points out of this. It was great that we got two. I really liked our effort, our drive and everything that came with it."

NOTES: The Lightning went with seven defensemen, with Slater Koekkoek making his season debut but playing sparingly (a game-low 3:09 of ice time). RW J.T. Brown, C Gabriel Dumont and D Andrej Sustr were healthy scratches for Tampa Bay. ... Washington played without three healthy scratches: D Christian Djoos and RW Tom Wilson, neither of whom has played this season, and C Tyler Graovac, scratched for the second time in three games.