While Randy Robitaille's slap shot ended Boucher's phenomenal string of five consecutive shutouts at 6:16 of the first period, the Thrashers ended their five-game road trip at 0-3-2.
Byron Dafoe made 40 saves as the Coyotes outshot the sluggish Thrashers 41-21.
"We played yesterday so the guys were a little weary in the third period," Atlanta coach Bob Hartley said, "and we did a good job just holding on at least for one point."
The Thrashers have an opportunity to pile up some points with seven of their next 10 games at home, but they might have a hard time starting the stretch off on a good note against the Canadiens.
Including two losses this season, Atlanta is just 3-13-2 all-time against Montreal, including a 1-6-2-0 mark at Philips Arena.
The Canadiens have won six of eight (6-1-1), including an 8-0 victory over Pittsburgh on Saturday.
"It was a different team," Garon said. "Defensively, I think we're playing great and we're not giving much, so it's easier for the goalie, especially with the great offense we had tonight."
Ribeiro scored his 10th goal of the season to tie it at 1-1 midway through the first period, and assisted on Richard Zednik's go-ahead goal 3:44 into the second. Ribeiro leads the Canadiens with 35 points in 44 games.
"It seems that whenever we need the break right now, it's going our way, and it's fun," said Koivu, who had two assists. "We've gone through some tough times in the last couple of years here so it's fun to have things going your way."