Five field goals by Phil Dawson had given the Browns a 15-14 lead with 5 minutes remaining, but Flacco guided the Ravens on a nine-play, 81-yard drive capped by the TD pass to Smith to wrest the lead.
Flacco overcame a slow first half to finish 15-of-24 through the air for 153 yards, and Ray Rice picked up 98 yards with a score on 25 carries for the Ravens.
Brandon Weeden completed 20-of-37 passes for 176 yards with two interceptions for Cleveland (2-7).
Trent Richardson compiled 105 yards on 25 carries in the loss.
Senate Democrats to pull all-nighter on climate change
Jessica Simpson shares three-way kiss with friends in photo