The Browns trailed Baltimore 23-24 in the AFC North slug fest with just over a minute to go in the fourth quarter.
The Ravens, who entered Sunday in sole possession of first place in the division, held a one-point lead after running back Derrick Henry's 2-yard run and Justin Tucker's point-after kick.
The Browns then started on their own 31, and Winston connected with wide receiver Cedric Tillman on a 2nd-and-15 for a 38-yard TD, Tillman's second score of the day.