Thomas Vanek also scored for the Sabres (34-20-9), who won for just the second time in their last 10 games to move a point in front of idle Ottawa for first place in the Northeast Division.
Simon Gagne and Mike Richards scored for the Flyers (33-26-4), who've lost two straight after stringing together five wins in a row. Michael Leighton finished with 32 saves, but lost for the first time in his last seven starts.
In overtime, Leighton was able to stop Buffalo defenseman Toni Lydman's shot from the left circle, but Connolly corralled the rebound in the low slot and lifted the puck up and in for the winner.
Richards broke a 1-1 tie with his 26th of the season with 8:51 left in the third. The Philadelphia captain picked off Connolly's pass at the Buffalo blue line and skated in alone before lifting the puck over Miller with a backhander that completed a nifty deke. Mair got the equalizer just under 3 minutes later when his backhander eluded Leighton's right shoulder.
The Flyers struck first when Gagne scored his 10th of the year 4 minutes into the second period. From in tight, Gagne was able to slip the puck past Miller off a feed from defenseman Lukas Krajicek from the left boards.
Vanek tied it 2:13 later with his team-leading 19th of the season. From the left corner behind the goal line, Vanek was able to bank a shot off Leighton's blocker and in.
NOTES: Lindy Ruff coached in his 965th career game with the Sabres, moving ahead of Jack Adams (Detroit) for third on the NHL list for games coached with one franchise. ... Sabres RW Drew Stafford missed the final two periods because of a lower-body injury. ... LW Raffi Torres played in his first game with the Sabres after being acquired at the trade deadline on Wednesday, and assisted on Connolly's winner. ... Vanek's goal gave him 300 career NHL points. ... Flyers C Jeff Carter played in his 277th straight NHL game, surpassing Bobby Clarke for the franchise's third-longest ironman streak.
