They went further in front thanks to DeMarco Murray, who rushed from four yards to put his team 13-0 in front before Bailey added another point.
The Broncos finally got themselves in the game thanks to their talisman Peyton Manning, who launched a pass for Julius Thomas to touch down with 50 seconds left in the opening quarter.
Dan Bailey sent a 43-yard kick between the posts to edge the Cowboys along early in the second quarter, but the tide completely turned thereafter, as Manning threw two more touchdown passes.
Eric Decker was the next man to profit from Manning's accuracy as he closed the gap to three points, before Thomas put the visitors in front with over three minutes left before half time.
Manning himself extended the lead to 11 points by rushing his first touchdown in five years, although Bailey reduced the deficit before the teams came in.