Joel Lindpere and Dilly Duka scored first-half goals and the Chicago Fire held on for a 2-1 victory over the Impact.
The win was the Fire's second straight and improved them to .500 this season (9-9-4), stretching an unbeaten streak to four games (3-0-1) in MLS competition. Coupled with New England's loss, Chicago climbed to sixth in the Eastern Conference.
"The second half was very good, we scored and we had a lot of chances," Schallibaum said. "But we have zero points and that's very disappointing."
The Impact (10-7-5) lost their second straight, falling behind Philadelphia to fourth place in the Eastern Conference. They have now lost four of their last eight matches.
"It's not easy to win away and Chicago is a good team," Schallibaum said. "But we must believe until the end and make the points. We have a good position, but we need more points than today."
The Impact's Felipe Martins cut the Chicago lead in half in the 57th minute, two minutes after entering the match. Martins drilled a 28-yard left-footed shot past Fire goalkeeper Sean Johnson for Montreal's only goal, and his fourth of the season.
Montreal's rally ended in the 94th minute, when Chicago forward Chris Rolfe headed Matteo Ferrari's header clear of the goal.
The Fire was explosive from the start, even with leading scorer Mike Magee missing the match with a tight right calf. Lindpere beat Montreal goalkeeper Troy Perkins in the sixth minute, his hard shot from the top of the penalty area deflecting off the Impact's Daniele Paponi for a 1-0 lead.
Duka made it 2-0 in the 23rd minute, kicking a low shot past a diving Perkins after beating three defenders on a 30-yard run. Duka was being tackled by Alessandro Nesta, the last of the trio, as he shot.
"It was a tale of two halves," Perkins said. "It was almost two (different) teams. We came out in the first half a little flat and they came out and pressed us and — fortunate for them — got two goals. The second half was the way we should have come out."
Johnson made five saves, including a close-range stop on Jeb Brovsky's one-hopper in the 89th minute.
Both teams had leading scorers sidelined Saturday.
Impact forward Marco Di Vaio (11 goals) was among seven reserves available and entered in the second half.
Chicago's Magee, the leading scorer in MLS with 14 goals heading into the match, was unavailable due to a right calf tightness while fellow forward Chris Rolfe was available but didn't start.
Both stepped out of league play last Wednesday. The Impact opened CONCACAF Champions League play with a 1-0 victory over San Jose while Chicago was knocked out of the U.S. Open Cup tournament by D.C. United.
The Impact have the week off before resuming MLS play next Saturday at Stade Saputo against D.C. United.