Drury won a faceoff back to Numminen, who ripped a drive that Drury knocked past goalie Henrik Lundqvist.
Thomas Vanek had a goal and an assist in fewer than 2 1/2 minutes of the second period, and Buffalo overcame two goals by Martin Straka to beat the Rangers for the third time. The Sabres won both Madison Square Garden visits this season in overtime.
Straka tied it with 4:53 left in the third period and nearly provided the late lift to the Rangers for the second straight night. He carried a pass from Michael Nylander into the left circle and ripped a shot over Ryan Miller's right shoulder.
Miller was sharp in making 25 saves for the Sabres, who avoided their first losing streak of the season and improved to 11-1 on the road.
Vanek set up Maxim Afinogenov's goal at 11:59 of the second period and then scored at 14:11 for the Sabres (19-3-2), who lead the Eastern Conference with 40 points. Buffalo had its NHL-record, 10-game road winning streak to start the season snapped at Ottawa on Nov. 18 but bounced back after a 2-0-1 homestand.