Cowboys quarterback Romo was intercepted five times, twice at the expense of touchdowns as Lance Briggs and Charles Tillman took advantage.
Robbie Gould's field goal broke the deadlock between the sides midway through the second quarter, shortly before Tillman returned an interception for the opening TD.
Miles Austin narrowed the gap after a 10-yard pass by Romo, before in the third quarter Devin Hester scored on a 34-yard pass from Jay Cutler and Briggs raced 74 yards for the second interception return touchdown.
Dallas could not get close on the scoreboard, and the game ran away from them as Brandon Marshall took a 31-yard pass from Cutler to score.
Jason Witten scored a late consolation for the well-beaten home side.