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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Stephen A. Smith says the Pittsburgh Steelers' season is done because the team is dysfunctional and looked horrible vs. the Chiefs in Week 2.
Panthers coach Ron Rivera says Cam Newton should feel safer under the NFL's new rules than he did two years ago when the quarterback criticized the league for not penalizing what he considered illegal hits on him.
Eagles quarterback Carson Wentz will start in Week 3 after being medically cleared just over nine months after tearing two ligaments in his knee.
The way Dallas punctuated its time-consuming, grind-it-out final drive with a touchdown reflected the identity it's trying to establish.
The Raiders may be down after their winless start, but focusing on the solid play of Derek Carr and Amari Cooper on Sunday should provide good vibes.
The veteran receiver didn't do much catching the ball, but Garcon's tenacious block, which sprung a long TD run, shows the attitude the 49ers need.