The Crew (9-6-13, 40 points) have four wins and a tie in the past five games although they were blanked for the 10th time.
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Chicago (8-13-8, 32 points) has been shutout in four straight games and are winless in five games (0-3-2).
Eloy Room made one save for his 10th shutout as the Crew moved 6-1-9 in the past 16 games.
The Crew is 9-0-4 at home vs. the Fire since 2013.
Columbus led 25-6 in shots but couldn't solve Slonina. The 18-year-old from Addison, Ill., will transfer to Chelsea of England's Premier League after the MLS season.
Slonina, who had five saves in a 0-0 tie against New England on Wednesday, made his third and best save of the first half in the second minute of stoppage time, diving to grab a strike by Derrick Etienne Jr. The Fire did not have a shot in target through 45 minutes.
The Crew kept knocking on the door. A Cucho Hernandez header off a corner kick missed by a few feet early in the second half.
In the 61st minute, the Crew was on the break and Lucas Zelarayan ripped a shot that Slonina somehow stopped. Two minutes later, Hernandez, who scored eight goals in his first eight games after joining the Crew in July but was scoreless in two straight, tested Slonina again to no avail.
Chicago's last goal was by Chris Mueller in the 49th minute of a 4-1 loss at Philadelphia on Aug. 13. That was followed by consecutive 2-0 defeats before the New England result.
Mueller had the Fire's first shot on goal vs. the Crew in the 73rd minute.