Ibrahimovic has made an immediate impact in California following his arrival from Premier League giants United, scoring twice in his match-winning debut against neighbours Los Angeles FC March 31.
And the 36-year-old Swede continued his inspired form for the Galaxy Saturday, scoring the winner in the first half at a sold-out Toyota Park in Chicago.
After Ola Kamara had two goals ruled out for offside in the opening stages of the match, Ibrahimovic broke the deadlock on the stroke of halftime when he headed Ashley Cole's cross past Fire goalkeeper Richard Sanchez.
"I think the game was difficult, it was not an easy game especially with the weather." Ibrahimovic said. "I mean, we come with the sun, they come with the wind, but the sun was the stronger today, so we’re happy."
It moved the Galaxy up to second in the Western Conference.
Schweinsteiger – another former United player – and his Fire have only won one of their opening five games to languish second from bottom in the Eastern Conference.
The Fire are only a point better off than reigning MLS champion Toronto, which suffered a 2-0 defeat against the Colorado Rapids.
Toronto reached the CONCACAF Champions League final during the week after upstaging seven-time winners America.
Head coach Greg Vanney prioritised Tuesday's first leg against Guadalajara by resting the likes of stars Sebastian Giovinco and Jozy Altidore against the Rapids, who took full advantage thanks to goals from Jack Prince and Shkelzen Gashi.
FC Dallas remains undefeated in the league following t 1-0 win over the New England Revolution, the Portland Timbers claimed a wild 3-2 victory against Minnesota United, the New York Red Bulls accounted for the Montreal Impact 3-1, 10-man D.C, United trumped against the Columbus Crew 1-0, and the San Jose Earthquakes and Houston Dynamo played out a 2-2 draw.