It was Ovechkin's 727th NHL goal, moving him within four of Marcel Dionne for fifth in history.
Justin Schultz had a goal and two assists, Brenden Dillon had a goal and an assist, and Lars Eller had two assists for the Capitals (26-11-4). Vitek Vanecek made 30 saves.
The Capitals lost 4-2 to the Boston Bruins on Thursday.
"Not the effort or the result we wanted last night. So it was important for us to come out tonight and get the two points," Schultz said. "I thought we played pretty well. There's some areas of improvement, but we got the job done. It was a tough back to back. And we can move on now."
Henri Jokiharju, Casey Mittelstadt and Tage Thompson scored, and Dustin Tokarski made 29 saves for the Sabres (9-25-6), who have lost two in a row after going 3-0-2 in their previous five games.
Dillon's slap shot from the point gave the Capitals a 1-0 lead at 2:39 of the first period.
Ovechkin made it 2-0 at 11:39 when his pass intended for Tom Wilson deflected off Sabres defenseman Rasmus Dahlin into the net. It was his 457th even-strength goal, passing Brett Hull (456) for sixth in NHL history.
Jokiharju cut it to 2-1 from the top of the left circle at 18:26.
Schultz scored from the top of the circles 28 seconds into the second period to make it 3-1.
"We were talking about it for a long time now, getting the pucks on the blue line and trying to create something in front of the net, and we did that today," Capitals forward Jakub Vrana said. "We got rewarded for it. Just overall game, I still think there are some windows we can still be better at, but like 'Schultzy' said, it was a big win for us, especially feeling good about going to the next game."