A fumble by Browns rookie Brandon Weeden on a sack appeared to put the Cowboys in control, but Romo gave it right back with a fumble on another sack.
The Cowboys made one goal-line stand in the final minutes, but the Browns (2-8) got another chance and went ahead 20-17 on Weeden's 17-yard pass to Benjamin Watson.
Dallas won for the first time in six games when Romo was sacked at least five times. He went down seven times, but still finished 35 of 50 for 313 yards with the touchdown to Bryant, who had 12 catches for a career-high 145 yards.
Referee Ed Hochuli carried on a running commentary in explaining replays and other rulings, and the most critical came in overtime when the officials ruled an incompletion on a throw that Miles Austin dropped and was not reviewed. The Cowboys were in position for a winning field goal, and replays appeared to show Austin had possession and took two steps before the ball was knocked out. The Browns recovered the loose ball.
Cleveland looked like the winner at halftime, leading 13-0 while Romo was running for cover and the crowd was booing repeatedly. But Dallas scored on its first three possessions of the second half and went ahead 17-13 midway through the fourth quarter on Romo's toss to Bryant.
Weeden fumbled on a sack by Anthony Spencer, who recovered. But Romo gave it right back when he fumbled as he was hit trying to scramble. It was his first turnover in three games.
Weeden took the Browns to the 1-yard line, but bruising running back Trent Richardson was stuffed on third down and Weeden threw incomplete with 1:42 remaining.
The Browns weren't finished, though. They used all three timeouts and forced a Dallas punt. The Cowboys' John Phillips was penalized for a horse collar tackle on Joshua Cribbs, even though replay to showed Phillips grabbing Cribbs' hair rather than his jersey. With the ball at the 17, Weeden found Watson in the middle of the end zone on the next play, just as he did for the game's first score.
After Cleveland went ahead, the Cowboys drove to the Cleveland 9 in the final seconds, keyed by a 35-yard pass interference penalty on Sheldon Brown. The Cowboys tried to throw into the end zone twice, then settled for Bailey's tying 32-yard field goal.
The Cowboys had finally scored on a 44-yard field goal with 5:44 remaining in third quarter, then abandoned an ineffective running game. Romo completed passes on the first seven plays, including a 30-yarder to Bryant, before Felix Jones went the final 2 yards on the ground to get Dallas within 13-10 early in the fourth quarter.
Dallas got the ball back quickly when safety Gerald Sensabaugh stuffed Richardson a yard short of a first down in the open field.
Richardson fell just short of becoming the first Browns rookie with three straight 100-yard games. He finished with 95 yards rushing, and added 49 yards receiving.
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Cowboys 23, Browns 20 (OT)
Cleveland 7 6 0 7 0 20
Dallas 0 0 3 17 3 23
Cle • Watson 10 pass from Weeden (Dawson kick), 4:01.
Cle • FG Dawson 51, 12:09.
Cle • FG Dawson 37, 5:07.
Dal • FG Bailey 44, 4:16.
Dal • F.Jones 2 run (Bailey kick), 13:54.
Dal • Bryant 28 pass from Romo (Bailey kick), 6:46.
Cle • Watson 17 pass from Weeden (Dawson kick), 1:07.
Dal • FG Bailey 32, :02.
Dal • FG Bailey 38, 6:07.
Attendance • 81,936.
First downs 19 30
Total Net Yards 311 320
Rushes-yards 33-119 21-63
Passing 192 257
Punt Returns 2-41 2-27
Kickoff Returns 5-54 0-0
Interceptions Ret. 0-0 0-0
Comp-Att-Int 20-35-0 35-50-0
Sacked-Yards Lost 2-18 7-56
Punts 5-44.6 7-43.1
Fumbles-Lost 2-1 1-1
Penalties-yards 12-129 9-92
Time of Possession 30:43 42:16
Rushing • Cleveland, Richardson 28-95, Hardesty 4-23, Ogbonnaya 1-1. Dallas, F.Jones 14-43, Dunbar 5-10, Romo 2-10.
Passing • Cleveland, Weeden 20-35-0-210. Dallas, Romo 35-50-0-313.
Receiving • Cleveland, Richardson 6-49, Gordon 5-53, Watson 4-47, Little 3-53, Cooper 1-6, Smith 1-2. Dallas, Bryant 12-145, Witten 7-51, Austin 6-58, Harris 3-20, F.Jones 2-12, Dunbar 2-6, Ogletree 1-10, Beasley 1-8, Vickers 1-3.
Missed Field Goals • None.