The Bears (2-4) blew a 14-point lead in the second half before coming through in overtime behind Howard, whose 53-yard run put Chicago at the Baltimore 40. After rookie Mitchell Trubisky completed an 18-yard pass to Kendall Wright, Barth delivered the game winner.
Making his first career start on the road, Trubisky directed a conservative game plan that leaned heavily on the run. The first-round draft pick completed 8 of 16 passes for 113 yards and a touchdown.
Howard had 36 carries and the Bears gained 231 yards on 54 attempts.
Baltimore (3-3) trailed 17-3 in the third quarter and 24-16 late in regulation before using two long kick returns to get back in the game.
Bobby Rainey took a kickoff 96 yards for a score to begin the comeback and Michael Campanaro brought back a punt 77 yards for a touchdown with 1:37 remaining. The 2-point conversion was successful, setting up overtime.
The Ravens weren't the only ones to capitalize on big plays. Chicago used a halfback pass from Tarik Cohen to Zach Miller for a first-half score, and Adrian Amos returned an interception 90 yards for a touchdown for a 24-13 lead with 5:08 left.
Chicago forced three turnovers and frustrated quarterback Joe Flacco throughout the afternoon. Operating without injured receivers Jeremy Maclin (inactive) and Breshad Perriman (second-quarter concussion), Flacco went 24 for 41 for 180 yards with two interceptions.
That put the Ravens in a precarious position, especially with a struggling offense.
Rainey alleviated the pressure by taking the ensuing kickoff for a touchdown. Rainey popped to his feet after being tripped by a teammate, broke right and went the distance.
The Ravens were coming off a 30-17 win in Oakland in which they did not commit a turnover, didn't allow a sack and were penalized only once.
In this one, Baltimore gave the ball away twice, permitted two sacks and was flagged five times -- in the first half.
Bears: Host Panthers, who will have a few extra days rest after playing on Thursday night.
Ravens: Face the Vikings on the road for the first time since 2009.
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