Aebischer made 31 saves and Chris Higgins got his third shorthanded goal of the season as the Canadiens defeated the Ottawa Senators 4-2 on Tuesday night.
Coach Guy Carbonneau said he will soon make a choice between Aebischer and last season's goaltending star Cristobal Huet as his top man.
"We have two good goaltenders, but some point soon we'll start riding one that's hot," said Carbonneau. "I don't know when, but we're close.
"David has been solid every game he's played this year. I think he's getting more confident every game. He makes saves look easy even when they're not."
Huet, the main reason Montreal made the playoffs last spring, has not been as sharp this season but has been stronger in recent games.
"We push each other to play well," said Aebischer. "There is a certain competition between us, but it's a healthy one that benefits us both and the team."
Aebischer's performance helped Montreal win a point on Saturday despite being outshot 51-22 in a 5-4 shootout loss to Toronto. He was even sharper against the Senators, who outshot Montreal 33-29.
Alex Kovalev also scored for Montreal (6-2-3) and Jason Spezza got one for Ottawa (5-6-0) before a three-goal outburst in the final 1:16 of play that saw Andrei Markov score into an empty net, Steve Begin get an insurance goal and Ottawa's Tom Preissing score with nine seconds to play.
For Ottawa, it was a familiar story of late - they win by blowouts and lose the close ones. They were coming off a 2-1 loss in Boston, after scoring 21 goals in three straight wins.
"I get the feeling we're getting discouraged," said defenceman Joe Corvo. "It seems like we don't know what to do in certain situations. - myself included.
"It's strange we're not scoring after getting 21 in three games. It's just an inconsistent effort again."
The Senators also dropped to 0-5 in games in which the opposing team scores first.
A turnover at centre ice by Spezza let Higgins go in alone and shovel a backhander one-handed under Ray Emery's pad 5:30 into the second period.
It was Higgins' sixth career shorthanded goal. He moved into a tie with Pittsburgh rookie Jordan Staal for the league lead with three this season.
"It's just intensity and anticipation," he said. "Some guys have it and some don't and that's why they're penalty killers."
Late in the second frame, the Canadiens killed off a 56-second two-man Ottawa and less than a minute later, Alexander Perezhogin won a race for a puck in the Ottawa zone that allowed Sergei Samsonov to slip it across the crease for Kovalev's tap-in goal at 18:32.
It was a second strong performance in a row for the recently formed Russian trio, but Carboneau was most impressed by Kovalev's back-checking.
"Our faceoffs weren't good (Kovalev won six and lost nine), but he was good," said Carbonneau. "When we lost the puck, he was always the first one back to help our defence"
Spezza cut the lead to one goal when he flipped a puck into the slot and saw it go off Radek Bonk's stick into the top corner 6:19 into the third frame.
Ottawa dominated the faceoff circle 40-24 overall, so it may not have been wise for Markov, with Ottawa playing with six attackers, to risk an icing call by firing the puck from behind his own goal-line.
But it went into the empty Senators' net with 1:16 left to play.
Begin got his first of the season at 19:03 after a turnover and Preissing got one back in the dying seconds.
Late in the third period, Montreal defenceman Mike Komisarek left with a sore right shoulder. The team will know more about his condition on Wednesday.
The Canadiens play in Carolina on Thursday, while the Senators' next game is also against the Hurricanes on Saturday in Ottawa.
Notes - D Wade Redden missed a second straight game for Ottawa. Coach Bryan Murray wants his groin healed before he returns. . . F Peter Schaefer returned after missing four games, bumping Alexei Kaigorodov from the lineup. . . Montreal F Aaron Downey returned after missing five games with a concussion. F Garth Murray was scratched. . . The Canadiens drew their 70th consecutive regular-season sell-out crowd of 21,273.