The hosts made a quick start to the match with a touchdown after less than three minutes, Todd Gurley running in from six yards for his fifth score in the last four games.
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It was the first rushing touchdown that the Bears had allowed since week two, but they restored parity almost immediately as Jay Cutler's short pass found Zach Miller, who burst between two defenders and ran all the way in for an 87-yard score.
Greg Zuerlein nudged his side back into the lead with a 26-yard field goal, although it could have been better for the hosts had Tavon Austin's touchdown not been nullified for offensive holding by Greg Robinson.
The visitors took the lead for the first time in the second quarter as Cutler found Miller in the middle of the endzone for a two-yard score, with the receiver claiming his second touchdown of the night and third in two games having managed just four in five years before this season.
Things got even better for John Fox's side shortly afterwards as Jeremy Langford collected Cutler's short pass before running home for an 83-yard score, making the Bears the first side to have more than one score of 80 yards in a game since 2006.
The Rams could not find a response before the end of the half, leaving them trailing by 14 at the interval.