Referee Tim Peel, parked behind the net, immediately ruled it a goal, which was confirmed after a video review.
Budaj wondered whether Peel could have blown the play dead a split-second earlier.
"The big question is whether the referee saw the puck," Budaj said. "I'm not blaming the referees or anything. It happened in a split-second and it was a matter of opinion."
Vanek never lost sight of the puck and dived into the pile of bodies hoping he could get a piece of it.
"I was patient. Once I saw it there, I just jumped at it and got a good whack at it," said Vanek, who knew time was running out. "I saw that black little thing and jumped on it. If the buzzer went, so be it."
The goals came late in a game in which Vanek thought he had squandered several scoring chances in the second period.
"I thought to myself that maybe it was one of those nights where it wasn't going to go in," Vanek said. "But I said, 'Stick with it.' As a team we stuck with it and we got rewarded."
The Canadiens appeared to take control when Plekanec scored on a breakaway 45 seconds into the third period to make it 4-2.
Subban made it 3-2 by one-timing a shot from the left circle with 1:28 left in the second. It came during a two-man advantage after Cody Hodgson (hooking) and Ott (high-sticking) were penalized 33 seconds apart.
Subban extended his point streak to four games (two goals, two assists), all coming since making his season debut in a 6-1 win over Buffalo last weekend after signing a two-year, $5.75 million contract.
NOTES: The Sabres went 1 of 7 on the power play and squandered their own two-man advantage that spanned 46 seconds early in the second period. ... Canadiens LW Travis Moen missed his first game of the season because of a lower-body injury sustained Wednesday. ... Montreal has scored a power-play goal in nine of 10 games. ... The Sabres are 117-101-37 against Montreal, their most wins against any opponent.