The Capitals won for the seventh time in eight games, improved to 9-3 in December, and maintained an eight-point lead in the Southeast Division.
Ovechkin, last season's MVP, stormed out of his own zone, tipped a pass ahead to himself, faked out a Buffalo defender at the blue line and then rocketed a shot on goal as he was falling to his stomach.
The puck sailed past Patrick Lalime for Ovechkin's 23rd goal, giving Washington a 3-1 lead with 11:33 to go.
Maxim Afinogenov brought the Sabres within a goal by scoring with 1:49 remaining.
Thomas Vanek produced Buffalo's first goal, giving him 25 for the season. That puts him one behind Jeff Carter of Philadelphia for the NHL lead.
Buffalo had won in its previous three trips to Washington.