The goals were the Poland captain's first for his new club, coming in his third appearance and his home debut.
The star striker levelled the match in the 20th minute, heading in a cross before finishing from the edge of the box.
He then put Chicago ahead in the 68th minute, running onto a through ball to score one-on-one with the goalkeeper.
"It was a very important day for me, and for the whole team, to win after two games without a victory. Today it was important to build confidence for the matches ahead," Lewandowski said afterwards.
The win was Chicago's ninth of the season, lifting them to fourth in the Eastern Conference with 29 points from 17 games.
Nashville SC top the table with 40 points from 18 matches, ahead of Inter Miami (38) and New England Revolution (30).
Chicago Fire face Portland Timbers in the MLS on 16 August, but first play Mexico's Necaxa in the Leagues Cup.
The Polish striker joined Chicago on June 29 after four seasons with Barcelona.
(ał)
Source: PAP, tvp.info