Heatley scored two goals 38 seconds apart to put Ottawa ahead with 7:59 remaining in the third period and the already-eliminated Senators dealt a big blow to Montreal's playoff chances with a 3-2 victory on Monday night.
Heatley lifted Ottawa into a 2-2 tie at 11:23 and then netted his 37th of the season at 12:01 when he beat Jaroslav Halak from the slot with a shot that silenced the sold-out Bell Centre crowd.
"I wish that we had the third goal back, the shot under the arm -- probably Halak does, too, but Heatley is a guy who scores 40 goals every year," Canadiens coach Bob Gainey said. "He gets them different ways and he got us tonight."
Chris Campoli also scored for the Senators, who will miss the playoffs for the first time in 13 seasons.
Alexei Kovalev netted his 25th goal, and Mathieu Dandenault scored with 3.8 seconds remaining in the second period for the Canadiens, who are seventh in the Eastern Conference but only three points above the playoff cutoff with three games left.
Montreal left for New York following the game for Tuesday night's matchup against the Rangers, who are tied with Florida in points right behind the Canadiens.
"We had the game in our control and we let it slip away but there are three games left. This game is over and done with now," Canadiens defenseman Josh Gorges said. "We have a big game [Tuesday night] that we have to focus our attention on."
"The players weren't available tonight and won't be [Tuesday night], but I have no more information to give you about the injuries to Markov and Schneider," Gainey said.
"I thought we cycled and took advantage of their D pretty good," Fisher said. "We got a couple of quick goals and then we just hung on."
Kovalev extended his point streak to seven games when he made it 1-1 at 12:46 of the second. He put a wrist shot from the right side past Alex Auld and into the top left corner, giving him eight goals during his scoring spurt.
Dandenault gave Montreal its only lead when he put a slap shot past Auld with only seconds remaining in the middle period.
Kovalev has 16 points in his streak since teaming up with Saku Koivu and Alex Tanguay to form the Canadiens' top line. Koivu and Tanguay each have 10 points, and the trio has combined for 36 since the line was put together during a 6-3 victory against Atlanta on March 24.
Campoli gave Ottawa a 1-0 lead with his 11th goal on a power play 10:56 into the second. The defenseman took Nick Foligno's centering pass and put a low shot through Halak's pads from the left edge of the crease as the Canadiens goalie slid to his right.
Montreal was awarded a penalty shot for a third consecutive game after Chris Higgins was hauled down while trying to put a backhander into a wide-open net with 51.2 seconds remaining in the first.
Auld stopped a shot by Higgins, who was given the free attempt after he outraced the Ottawa goalie for a loose puck, only to be hauled down by Ryan Shannon and Nick Foligno as he put a backhander wide on a shot at an open net.
Doug Janik was called up from the Hamilton of the AHL and made his Canadiens debut, paired with Ryan O'Byrne, as Montreal tried to offset the loss of Markov and Schneider. Janik was acquired on Feb. 26 from Dallas, where he had played 13 games.
"Obviously guys are going to be playing more minutes, playing different roles and different situations, so we have to rise to the occasion and make sure we step up our level of play," Gorges said.
- Ottawa allowed a penalty shot for a second successive game. Philadelphia's Darroll Powe scored on Auld in the Senators' 4-3 overtime victory Saturday.
- Montreal's Patrice Brisebois received a silver stick from Hall of Famer Henri Richard in a pregame ceremony honoring the veteran defenseman's 1,000th regular-season game. Brisebois reached the milestone in a 3-1 loss to New Jersey on March 14, the same night Devils goalie Martin Brodeur tied Patrick Roy's career NHL record for regular-season victories.