Max Pacioretty scored the winner in the 3, on Friday.
"Those are points that we desperately want and need and I think we deserved it tonight," Canadiens interim coach Randy Cunneyworth said. "It's nice to get the reward."
On Thursday, the Sabres squandered a two-goal lead in an eventual 7-2 loss the Flyers. Against Montreal, they were again up early, leading 1-0 less that five minutes in on Regehr's long slap shot, but couldn't hang on.
Kaberle tied just after the midway point of the first, diving in from the weak side and burying a feed in front from Desharnais.
The Sabres were back on top at the 15:43 mark when a scramble in front resulted in a loose puck and Myers was there to send it home.
Gomez ensured a tie at the first intermission, as his slap shot from the right circle found the back of the net with one second left on a power play and 14 seconds left in the period.
The Canadiens took the lead, 3-2, near the midway point of the second when Campoli found himself open between the circles and sent a high wrister past Miller.
Ennis ensured overtime with 8:05 left in the third. He sat at the top of the crease and Ville Leino found him from behind the net for the equalizer.
"No excuse not to get two points right there," said Miller. "We had opportunities and I need to make a save at some point in the shootout."
This was the fourth of six meeting between the teams this season. Buffalo had won the first three and six straight overall...The Canadiens have scored 19 goals over their last five games...Montreal was 1-for-2 on the power play while Buffalo was 0-for-3.