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.
Baltimore was in position for the go-ahead score when Amos got his first career interception on a pass that bounced off the chest of receiver Chris Moore, who was covered tightly by Kyle Fuller.
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.
Trubisky put Chicago ahead 17-3 in the third quarter with an on-the-run, 27-yard touchdown pass to tight end Dion Sims, who outfought Tony Jefferson for the ball in the end zone.
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.