Batherson tied it 2-2 at 3:04 of the third period when he redirected Brady Tkachuk's centering pass for a power-play goal.
The Capitals took four minor penalties in the third, but the Senators finished 1-for-6 with the man-advantage.
"It's great that we found a way, a different way, to get the two points," Ovechkin said. "It was a tough third period, but our penalty kill did a great job to keep us in the game, and [Kuemper] was solid today."
Ovechkin nearly scored No. 801 midway through the third when his snap shot from the slot was denied by Talbot's outstretched left pad.
He had six shots on goal and has 6,211 in his NHL career, which moved him past Ray Bourque (6,209) for first on the all-time list.
"It probably goes hand-in-hand, right? You've got to deliver the puck in order to be up there in goals," Capitals coach Peter Laviolette said. "That's no surprise. Impressive, though. He could be tops of the charts in shots, goals and hits. That's pretty impressive."
Ovechkin will try for No. 801 again Friday when the Capitals host the Winnipeg Jets.
"It'll come," Laviolette said. "He's just got to keep doing what he's doing."