The Braves were ahead 1-0 in the eighth inning and looking to clinch the National League East crown when Chicago struck for three runs.
That brought up Anthony Rizzo, who laced a double into the left-field corner for a score-tying RBI.
Dave Carpenter took the mound, only to be greeted by Navarro's decisive RBI single to right.
Nate Schierholtz capped the rally with a sacrifice fly.
Medlin yielded just one run on six hits over 7 1/3 innings for the Braves, whose magic number to claim the NL East remained at one.