Less than two weeks after leaving Manchester United and moving to Chicago, Schweinsteiger played all 90 minutes and scored the opening goal with a header following a corner kick in the 17th minute.
The Impact equalized through Matteo Mancosu just after the hour mark, and it got worse for the Fire after Juninho was sent off for a second booking 10 minutes later.
Montreal's Victor Cabrera was also sent off 10 minutes from time for bringing down Luis Solignac, who had been played through on goal by the influential Schweinsteiger.
The German volleyed narrowly wide after a corner as he looked to inspire his new side to victory, but the Fire instead fell behind as Ballou Jean-Yves Tabla struck in the 90th minute.
But there was still time for Solignac to rifle in an equalizer for Chicago to ensure Schweinsteiger did not start his American adventure on a losing note.
"It's a great moment when in your first match you score a goal, though I'd rather have a win," Schweinsteiger told CSN after the game. "I think we deserved the draw. We had good chances, but we didn't finish."
Christian Ramirez scored twice as Minnesota United won their first-ever game in MLS, 4-2 over Real Salt Lake.
After Luke Mulholland fired Real Salt Lake in front after just four minutes, it looked to be more of the same for the expansion club, which had conceded 18 goals in its first four games in the league.
But Kevin Molina equalized with a header in the 16th minute before Ramirez took over over in the second half.
His first came in the 52nd minute after he was played in by Molina, and his second 10 minutes later following a mistake from RSL keeper Nick Rimando, who misplayed the ball outside his penalty area.
Johan Venegas scored Minnesota's fourth after Justin Schmidt gave the ball away in his own half for RSL, who got a late consolation goal from Yura Movsisyan.
Erick "Cubo" Torres scored a hat trick to help the Houston Dynamo overcome an early deficit and beat the New York Red Bulls 4-1.
Bradley Wright-Phillips opened the scoring for the Red Bulls after making a curling run in the 13th minute, but the Dynamo equalised less than two minutes later through Dylan Remick's header following a corner.
Torres got his first of the night from the penalty spot in the 41st minute after Damien Perrinelle brought down Mauro Manotas. He then scored his second in the 56 minute, recovering after completely missing a volley to curl a shot in the net.
Torres saved the best for last, scoring from a free kick in the 91st minute to become the first Mexican to record a hat trick in MLS since Jose Vasquez in 1997.
Visitors LA Galaxy were powerless to stop a second-half blitz from theVancouver Whitecaps, who ran out 4-2 winners atBC Place.
A four-minute brace fromRomain Alessandrini had the Galaxy 2-1 up at half time afterCristian Techera opened the scoring for Vancouver.
ButFredy Montero broughtMike Rabelo's men level in the 66th minute, poking home from six yards.
Matias Laba then got the go ahead goal with a fine low drive from outside the box, before bagging himself a brace of his own in the 87th minute.
TommyMcNamara came off the bench to score for New York City FC in a 2-1 win over the San Jose Earthquakes.
Marcos Urena had put San Jose ahead just six minutes in afterSean Johnson misplayed a back pass from Andrea Pirlo.
But NYCFC were back level four minutes later when David Villa back-heeled a pass into the box for Jack Harrison, whose shot struck goalkeeper David Bingham but crept over the line.
McNamara came on forAndrea Pirlo in the 63rd minute and scored the winner four minutes later, slotting home afterRonald Matarrita pulled the ball back to set up his teammate from 15 yards.
The Earthquakes' hopes of salvaging a draw were squashed whenVictor Bernardez was sent off for kicking out atMcNamara with 10 minutes to play.
Justin Meram scored a goal in each half and Columbus Crew SC beat Orlando City 2-0.
In the 13th minute, Meram, who has three goals and two assists in five games for Columbus, raced in the open field to get to a chipped pass and powered a shot off the hands of goalkeeper Joe Bendik.
Meram scored on another counter-attack in the 77th minute. He settled Federico Higuain's pass at the corner of the 18-yard box, took three touches and cut it back to get an angle for a back-post shot.
The best scoring chance for Orlando came in the fourth minute of second-half stoppage time on Will Johnson's shot that went just wide.
Jose Guillermo Ortiz and Luciano Acosta put through first-half goals and D.C. United hung on to beat the Philadelphia Union 2-1.
United's first win of the season snapped a three-match winless streak against Philadelphia dating back to July 2015.
Ortiz found the net first, taking advantage of a Union turnover in their own zone to give D.C. their first goal of the season in the 18th minute. After making a save, Union goalkeeper Andre Blake's pass to Fabinho was mishandled, ricocheting off his head to Lloyd Sam, who promptly found Ortiz for the goal.
Acosta added the second goal nine minutes later from a penalty kick after the Union were called for a handball in the box.
Philadelphia got on the board in the 71st minute when C.J. Sapong scored from a rebound after Alejandro Bedoya's shot was saved by Bill Hamid, who also made a spectacular late stop of a Sapong shot to preserve the lead.
Chicago 2-2 Montreal Impact - Via MLS
Bastian Schweinsteiger entered MLS with a bang, opening the scoring against Montreal before they ultimately drew 2-2.
Minnesota 4-2 Real Salt Lake - Via MLS
Minnesota turned the tide on their difficult start to life in MLS, downing RSL convincingly for their first-ever league win.
Torres' free kick seals hat trick - Via MLS
Cubo Torres buries a free kick to complete a hat trick and continue Houston's rout of New York Red Bulls.
Vancouver Whitecaps 4-2 LA Galaxy
Matias Laba led a second-half surge that saw Vancouver overcome a 2-1 halftime deficit to beat LA Galaxy.
NYCFC 2-1 SJ Earthquakes - Via MLS
NYCFC completed the comeback win at home against a feisty San Jose, with David Villa nabbing two gorgeous assists.
Columbus 2-0 Orlando City - Via MLS
Justin Meram struck twice as Columbus continued their hot start with a win over Orlando City.