Jared Goff was intercepted four times, sacked three times and held to just 180 passing yards and no touchdowns.
Star running back Todd Gurley gained just 28 yards on 11 carries.
The Rams (11-2) missed a chance to secure a first-round playoff bye and fell into a tie with New Orleans for home-field advantage throughout the NFC playoffs.
The Bears' Eddie Goldman led the defensive effort, including getting to Goff for a tiebreaking safety early in the third quarter.
Bradley Sowell became the first Bears offensive lineman in 11 years with a touchdown reception when he caught a 2-yarder from Mitchell Trubisky in the third quarter.