The Browns / Cowboys rivalry has been played 32 times (including 3 postseason games), with the Cleveland Browns winning 18 games and the Dallas Cowboys winning 14 games. Dak Prescott discusses how the Dallas Cowboys played complementary football and who were key contributors in their 30-10 win over the Jets. > Cleveland Browns at Dallas Cowboys - November 18th, 2012. The following is a list of all regular season and postseason games played between the Cleveland Browns and Dallas Cowboys. Dallas Cowboys, 2013) On October 6, 2013, the Dallas Cowboys hosted the Denver Broncos for a game in which 99 total points were scored, tied for fifth-highest in NFL history. All other NFL-related trademarks are trademarks of the National Football League. The National Football League playoffs for the 1980 season began on December 28, 1980. Cleveland Browns 20 at Dallas Cowboys 23 on November 18th, 2012 - Full team and player stats and box score. The game ended when placekicker Norm Johnson converted a 42-yard field goal with 1:46 left in overtime. NFL and the NFL shield design are registered trademarks of the National Football League.The team names, logos and uniform designs are registered trademarks of the teams indicated.