Cutler was 21 of 29 for 277 yards and outdueled Tony Romo (34 of 51, 374 yards, TD), who threw two interceptions. Dallas also lost the ball on a fourth-quarter fumble and fell to 0-2 for the first time in nine years.
"Any time you get in this position it's very difficult," Romo said. "We've got to climb our way out of this. … It's frustrating. We've got to do things better. And we need to figure it out in a hurry."
David Buehler kicked a 28-yard field goal to trim the Cowboys' deficit to 20-17 in the third quarter but hooked a tying 44-yarder wide left midway through the fourth.
The Bears extended their lead to 10 when Devin Hester (four receptions, 77 yards, TD) caught a short pass, eluded a defender and raced 38 yards to the Cowboys' 3. Cutler and Matt Forte hooked up for a TD on the next play with 5:16 left.
"It was a signature game," Bears coach Lovie Smith said. "We just made plays throughout."
Rookie Dez Bryant returned a punt 62 yards for a touchdown to give Dallas a 7-3 lead late in the first quarter.
The Bears answered when Cutler hit tight end Greg Olsen over the middle, and he took it 39 yards for a score.