Cowboys quarterback Tony Romo was able to pass for 506 yards including five touchdown passes during the clash.
The team's executive vice-president of football operations told the club's official website: "If you look at the first four games compared to the last game, obviously we weren't in a dog fight in the first four. We started out that way but we kind of ran away from everybody in the second half. This one was a dog fight.
"We didn't have our best, our 'A' game. And even though offensively we played well, we slowed down in the second half and defensively struggled a little bit. But a lot of that credit goes to Tony Romo and the Dallas Cowboys offense and the fact that the played very well.
"They made a bunch of big plays. They kept battling. So it was a good win for us. We made a lot of mistakes on both sides of the ball and so hopefully we'll get that cleared up."
The Broncos face the Jacksonville Jaguars this weekend.