Cutler completed 21 of 29 pass attempts for 277 yards to lead the Bears, while Cowboys quarterback Tony Romo hit 34 of 51 for 374 yards but squandered several scoring opportunities.
It was Chicago's second straight win this season while the Cowboys, who were beaten 13-7 by the Washington Redskins on Sunday, slipped to 0-2 for the first time since 2001.
"Anytime you get in this position it's very difficult," said Romo. "We've got to climb our way out of this.
"You sit there and you wonder if you're ever going to win a football game when you get to this point. That's not what you'd expect going into the season.
"It's frustrating. We've got to do things better. And we need to figure it out in a hurry."
Watched by a crowd of 85,168 at Cowboys Stadium, Dallas outgained the Bears 410-308 in total yards and held a 23-14 edge in first downs.
But the Cowboys paid the price for an overall sloppy display.
Romo threw behind his receivers several times and tossed two interceptions, both of which led to Chicago field goals.
Midway through the fourth quarter, the Cowboys wasted a chance to tie the game at 20-20 when kicker David Buehler badly missed a field goal from 44 yards.
Cutler responded by hitting running back Matt Forte for a three-yard touchdown.
Buehler made it 27-20 with a 48-yard field goal with 1:28 remaining but it was a case of too little too late for the stumbling Cowboys.
Going into this season, Dallas had been widely expected to make the playoffs, where they will try to become the first team to play the Super Bowl in their home stadium.
"We've got to stay together," said Phillips. "We can move the ball. We can play defense. And we can play special teams. We can do those things.
"But we've got to put it all together."
(Writing by Mark Lamport-Stokes in San Diego; Editing by Steve Ginsburg)