Ovechkin scored 40 seconds into the game and added an empty-net goal with one second remaining to help the Capitals earn a 5-3 win against the Lightning at Amalie Arena on Tuesday.
"We had to have a good start, especially against this team," Ovechkin said. "I think we played well; physically put the puck in the net and we got the result."
Brooks Laich scored at 4:36 of the second period to give the Capitals a 3-2 lead. He controlled a loose puck after it bounced off the glass near the right post and sent it past Lightning goalie Ben Bishop.
Troy Brouwer gave the Capitals a 4-2 lead with his seventh goal of the season at 10:52 of the third period when he came in as a trailer on an odd-man rush and fought off a check attempt by Steven Stamkos to flip the puck high past Bishop.
"We needed to play simple, stay focused all the time, and it was a great result for us," Ovechkin said. "We won a game against a great team. Mentally, that's really important for us.
The Capitals (13-10-4) won all three games on their road trip. The Lightning (18-8-3) have lost three of four. They play each other again Saturday at Verizon Center.
"We had our chances, we had power-play opportunities, it just didn't go in the net," Lightning coach Jon Cooper said. "Sometimes they're going in for you and sometimes they are not, and it's too bad because it cost us."
Stamkos scored his 250th NHL goal 47 seconds into the second period to tie the game 2-2. The Lightning captain took a centering pass from Ryan Callahan and sent a wrist shot past defenseman Brooks Orpik and between the pads of goalie Braden Holtby.
"We're not playing the way we need to in order to be successful," Stamkos said. "Maybe we're not getting some bounces that we were getting at the beginning of the year, but we've got to earn those. We got behind the 8-ball again on the first shift."
Holtby made several key saves in the third period. He stopped Lightning forward Nikita Kucherov on two opportunities in front of the net early in the period and finished with 33 saves.
Late in the second period the Lightning almost tied the game on a power play, but Valtteri Filppula's shot hit the post and Holtby smothered the puck and fell into the net. The referee blew the whistle and signaled no goal with a video review confirming his call.
"You have to keep putting the puck on the net and hope that a few go in," Filppula said. "It's a long season and you're going to have ups and downs, and now we have two games we've lost against good teams (3-1 to the Columbus Blue Jackets on Saturday). I feel like we will fix a few things and hopefully get our power play working as well."
The Lightning were 0-for-4 for their power play, including three consecutive in the second period.
"When you get three straight chances you have to get a goal," Lightning defenseman Victor Hedman said. "We had some good looks and got closer and threw it in the post, but obviously that's a tough one to swallow."
"We certainly weren't perfect tonight," Niskanen said. "[Holtby] had to make probably more saves than we would like on a normal night … it was a good team effort though, we were assertive with our play. We were really strong on pucks in the right areas and scored some timely goals. We found a way to win against a team that scores a lot of goals."
Tampa Bay's Brian Boyle scored at 13:49 of the first period, and Filppula scored with 2.9 seconds remaining in the third.
"You can't accept these results because we want to take care of the home ice," Boyle said. "They got off to a good start and we couldn't match it. We're going to go on to the next game (Thursday at home against the Carolina Hurricanes), but it's disappointing to lose back-to-back games at home."