The Fire went up a man in the 53rd minute whenDeian Boldor was shown a red card following a video review for a late, studs-up challenge onSchweinsteiger.
And the former Germany star got his revenge six minutes when he slammed home a first-timed shot from Matt Polster's cross.
However,Schweinsteiger later limped out of the game while grabbing his quad with an apparent injury.
Montreal's Ignacio Piatti hit the post in the 80th minute, but there was to be no equalizer for the Impact, who were playing without six players away on international duty.
The Fire snapped a four-game losing streak to move into third place in the Eastern Conference The Impact stayed just outside the playoffs, level on points with Atlanta United, who have two games in hand.
Kei Kamara scored his first career hat trick to lead the New England Revolution to a 4-0 win over Orlando City.
After Kamara volleyed in Scott Caldwell's cross from close range in the first half, the Revolution thought they had a second goal from Lee Nguyen, but the goal was correctly ruled out after video review for offside in the buildup.
Kamara added a second goal in the 75th minute, and five minutes later Orlando were reduced to 10 men as Jose Aja picked up his second booking.
The hat trick was complete in the 89th minute as Kamara ran in on goal and slotted in his 11th of the season.
He was then replaced by new signingKrisztian Nemeth, who marked his Revs debut by sliding a pass across for Teal Bunbury to add a fourth in stoppage time.
The Revolution moved up to eighth in the East, though they are still four points out of the playoff places.
FC Dallas managed a 2-2 draw with the New York Red Bullsand nearly won it despite playing a man down for almost an hour.
Jacori Hayes picked up his second yellow card in just the 37th minute after going in late on Connor Lade, andSacha Kljestan put New York ahead six minutes later after a fine back-heeled pass from Bradley Wright-Phillips.
Dallas equalized nine minutes into the second half as Michael Barrios played in Hernan Grana, but the Red Bulls again went ahead three minutes later whenAaron Long headed inKljestan's lob from a set piece.
But Dallas struck back after Lade brought down Barrios in the box and Diaz scored the resulting penalty, and the hosts came close to a winner in a mad scramble in stoppage-time, but Walker Zimmerman's header hit the post.
The Red Bulls stayed fifth in the East, while Dallas stayed sixth in the jam-packed Western Conference playoff race.
Romain Alessandrini and Gyasi Zardes each had a goal and an assist to help the LA Galaxy beat the Colorado Rapids 3-0 and snap a 10-game winless streak, including four consecutive losses.
Los Angeles won for the first time since a 3-1 victory at Colorado on June 21.
Alessandrini converted from the spot in the 18th minute after Zardes drew a penalty on goalkeeper Zac MacMath. Emmanuel Boateng blasted a left-footer, off a header from Zardes, from the top of the box to make it 2-0 in the 23rd minute. Zardes capped the scoring in the 56th minute, tapping Alessandrini's cross into an open net from point-blank range.
The Rapids have lost have lost four in a row since Steve Cooke was named interim head coach, replacing Pablo Mastroeni, on Aug. 15 and are winless in their last nine.
Jon Kempin had two saves and his second-career shutout.
Sigi Schmid, who was named the Galaxy's head coach on July 27, got his first win with team since 2004. He was named MLS Coach of the Year with Los Angeles in 1999 before winning the Supporters' Shield and the MLS Cup with the club in 2002.
Montreal 0-1 Chicago: Schweini seals it - Via MLS
The Chicago Fire earned three huge points on the road to a conference rival thanks to Bastian Schweinsteiger's lone goal.
Revolution 4-0 Orlando City: Kamara lights up - Via MLS
Kei Kamara scored his first ever MLS hat-trick en route to New England's crushing 4-0 win over conference foes Orlando.
FC Dallas 2-2 Red Bulls: 10-man Dallas rally - Via MLS
Despite playing with 10 men for 53 minutes, FC Dallas rallied twice to draw the visiting New York Red Bulls.
Galaxy 3-0 Rapids: LA's winless run ends - Via MLS
Romain Alessandrini and Gyasi Zardes starred as the LA Galaxy dispatched Colorado and snapped a 10-game winless streak.