Inter Miami (12-4-8) evened the score three minutes into the second half when Messi sent the ball Casemiro's way off a free kick for his third goal in his eighth MLS appearance. Casemiro's goals have come on headers in three straight matches.
Chicago (11-6-6) jumped in front in the 10th minute on a goal by Robert Lewandowski - his sixth in his first nine MLS matches. Defender Andrew Gutman picked up his sixth assist and Robin Lod notched his fourth as the Fire took the lead into halftime.
Chris Brady had six saves for Chicago. Brady made a diving save on a shot by German Berterame in the 16th minute - one of three first-half saves to keep the Fire in front.
Dayne St. Claire saved two shots for Inter Miami, which has gone 1-2-4 since the start of August.
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Messi also has 18 goals and is the first player in league history with 30-plus goal contributions in three separate seasons.
Inter Miami started the day in second place in the Eastern Conference - 10 points behind Nashville SC. Messi and company are trying to become the first team to win back-to-back championships since the 2011-12 Los Angeles Galaxy.
