Briere beat goalie Kevin Weekes to the glove side on a rush to give the Sabres their fifth win in a game in which they trailed by at least two goals. Buffalo also avoided its first losing streak of the season. The Sabres (12-1-1) failed to earn a point for the first time Saturday in a 4-1 defeat against Toronto.
Jaromir Jagr scored a goal and had two assists to take the NHL lead with 23 points, though the Rangers captain appeared to re-injure his surgically repaired left shoulder when he landed awkwardly on his left elbow trying to stickhandle around Brian Campbell in overtime. Jagr skated to the bench and didn't return before Briere's fifth goal of the season.
The Rangers have lost three straight on home ice.
Thomas Vanek opened the scoring at 3:18 of the first period with a left-post wraparound through Rangers defenceman Aaron Ward. The goal, Vanek's eighth, came on Buffalo's second shot of the game against Weekes, who started for the third consecutive game.
Jagr answered in the first minute of the second period with the first of three consecutive power-play goals scored by the Rangers. Jagr blasted a one-timer from the left circle against the grain and beat goalie Martin Biron to the glove side with a shot that rang off the right post.
Taking advantage of a parade to the penalty box that included a full 5-on-3 advantage with Jochen Hecht and Briere whistled for hooking and tripping on the same play, the Rangers made it 2-1 on Petr Prucha's fourth goal. Jagr fired a point shot through traffic and Prucha, on the left post, swept the puck past Biron for the Rangers' first lead.
The Buffalo penalties continued to mount, and with Ales Kotalik off for slashing, Michael Nylander scored on the Rangers' third consecutive advantage for a 3-1 lead midway through the middle period. Jagr earned his second assist and third point when he found Nylander in front of the net off a curl around the net.
Buffalo took advantage of Ryan Hollweg's hooking penalty four minutes later and cut the deficit to 3-2 on Briere's hard shot from the left circle.
Weekes made the save of the game on Buffalo's next shot when he snatched Drew Stafford's shot with his glove.
Buffalo tied it 3-3 at 8:13 of the third when Jason Pominville scored his ninth goal. He crashed the net on Briere's toss in transition from the left point.
Notes: Buffalo RW Maxim Afinogenov, who left Saturday's loss against Toronto in the first period with an injury believed to be a separated shoulder, didn't play. ... The Sabres recalled forwards Stafford and Daniel Paille from Rochester of the AHL before the game. ... Prucha left the game late in the second period when he was hit in the face by Jaroslav Spacek's clearing attempt. Prucha returned in the third with a full face shield. ... Buffalo D Nathan Paetsch was also hit in the face with a puck minutes earlier. ... Rangers C Martin Straka recorded his 400th career assist on Nylander's goal. ... Jason Ward of New York played in his 200th NHL game.