Deshaun Watson connected with Jerry Jeudy on a 33-yard pass to the Baltimore 29-yard line with 22 seconds remaining to set up the decisive kick.
Szmyt’s initial attempt from 42 yards was blocked by Keyon Martin, who was flagged for offside. Szmyt then drilled his second shot through the uprights.
Carson Schwesinger racked up 13 tackles and forced a fumble for the Browns (4-2), who are tied with the Ravens (4-2) atop the division.
Audric Estime rushed for a touchdown five days after the Browns signed him off the practice squad of the Minnesota Vikings due to starter Quinshon Judkins (knee) ailing. Judkins was eventually ruled out of the contest.
Watson was 16-of-26 passing for 164 yards as Cleveland halted a three-game slide against Baltimore.
Tyler “Snoop” Huntley started for the Ravens in place of two-time NFL MVP Lamar Jackson (ankle) for the second straight week. He completed 19 of 31 passes for 165 yards and one touchdown.
Josh Cuevas caught a scoring pass for Baltimore and Derrick Henry rushed for 58 yards on 17 carries but lost a key fumble.
Baltimore still led by seven when Tyler Loop was wide left on a 49-yard field-goal attempt with 14:13 left in the game.
Less than two minutes later, the Ravens had the ball again and Henry was forced to fumble by Schwesinger. Tyson Campbell recovered the ball at the Ravens’ 35 with 12:36 left in the contest.
Seven plays later, Estime scored on a 2-yard run to tie it at 10 with 8:33 remaining.
Cleveland had a chance to take the lead later in the quarter but Szmyt narrowly missed wide left from 48 yards with 3:40 remaining. That ended a streak of 25 straight makes for Szmyt dating back to last season.
The Ravens opened the game with an 11-play, 66-yard drive that featured Henry runs of 11 and 17 yards. The touchdown came when Cuevas was wide open in the middle of the end zone to make the 2-yard catch from Huntley with 8:11 left in the opening quarter.
Baltimore increased its lead to 10 when Loop connected on a 34-yard field goal with 4:37 remaining in the opening period.
The Browns had just 46 yards and three first downs in the first half.