McCown completed 19-of-31 passes for 216 yards and a touchdown for Chicago (6-4), which was trailing 10-0 in the first quarter when the game was delayed nearly 2 hours by severe weather.
Fans were evacuated into the Soldier Field concourses after strong winds, rain and lightning blew through downtown Chicago.
When play resumed, defensive end David Bass returned an interception 24 yards for a score to key the comeback, which lifted the Bears into a first-place tie with Detroit in the NFC North.
Matt Forte racked up 125 total yards with a receiving touchdown.
Ray Rice rushed for a season-best 131 yards with a score on 25 carries for the Ravens (4-6), who fell for the fourth time in five games.