Dan Bailey kicked a winning field goal with a little over 6 minutes left to play in OT after a 20-yard punt return by Dwayne Harris put the Cowboys on the Browns side of the field.
A pass interference call on Sheldon Brown gave the Cowboys the football inside the Browns' 15-yard line but they were unable to punch it in for a score. They settled for a field goal to send the game to overtime.
Cleveland failed to convert on a fourth-and-one play from the Cowboys one-yard line. They followed that by stopping the Cowboys on three-consecutive plays to force a punt. Brandon Weeden then hit Benjamin Watson on a 19-yard touchdown throw on the team's first play following the punt.
Tony Romo gave the Cowboys a four-point lead on a 28-yard touchdown pass to Dez Bryant.
The Cowboys capped off their third-quarter drive at the beginning of the fourth quarter on a two-yard Felix Jones touchdown run.
Dallas drove down the field easily with their first possession of the second half. That was until a Cleveland sack and holding penalty on subsequent plays pushed the team back and forced them to settle for a 44-yard Dan Bailey field goal.
Phil Dawson hit a 51-yard field goal, his 24th straight made attempt, after Brandon Weeden sailed a pass over the head of a wide open Josh Cooper deep in Cowboys territory.
Dawson's second field goal, his 25th straight, was a 47-yarder that came after a Browns' drive stalled.
Cleveland's first score came when Browns quarterback Brandon Weeden found Benjamin Watson in a soft spot of the coverage for a 10-yard touchdown pass on 3rd and Goal play. There were three defenders but the rookie QB put it right on the money to give Cleveland an early lead.