Buffalo, which reached the Eastern Conference finals last season, is off to its best start since winning its first eight games of the 1975-76 season.
The game was played despite the region still recovering from a crippling snow storm that began late Thursday night. Nearly 350,000 households are still without power in Buffalo and its surrounding suburbs.
The power outage, however, didn't seem to affect the sellout crowd, as there were few no-shows.
Daniel Briere had a goal and two assists, and Ales Kotalik, Maxim Afinogenov, and Jochen Hecht each scored.
Brendan Shanahan had two goals, and Martin Straka and Fedor Tyutin also scored for the Rangers, who lost their third straight game.
Trailing 2-0, the Sabres began their offensive onslaught when Kotalik scored his first goal of the season with five minutes left in the first period. Drury and Briere then scored 1:16 apart late in the first to give Buffalo a 3-2 lead.
The Sabres were outshot by an 11-1 margin in the first 15 minutes before outshooting the Rangers by a 10-1 edge over the final five minutes of the period.
Afinogenov and Hecht each scored to start the second to give Buffalo a 5-2 advantage before Shanahan scored his sixth goal to cut the lead to 5-3.
Drury followed with two goals 1:04 apart to give Buffalo a 7-3 lead after two periods. His third goal, and sixth of the season, came on the power play when he outmuscled New York defenceman Aaron Ward to a loose puck in the crease, sliding it past Rangers goalie Kevin Weekes.
Weekes was making his first start for the Rangers.
Buffalo goalie Ryan Miller won his fourth game, making 19 saves.
It was the third time this season that Buffalo has come back from a two-goal deficit to win.
Notes: The Rangers were originally scheduled to arrive in Buffalo on Friday, but changed their plans and came into the city on Saturday instead. ... The Sabres had no problems arriving from Detroit, where they played Friday night. ... Both Drury and Shanahan have points in all five of their games this season, and both have scored in three straight. ... Drury's four points tied a career-high. ... The Sabres donned their retro-blue uniforms that they wore from 1970-96.