"We just kept plugging, we knew we had some good stuff," Cutler said. "We just had to figure them out."
Cutler threw three TD passes to Brandon Marshall, two in the wild fourth quarter, as Chicago erased a 13-point deficit and quieted the sellout crowd. Cutler threw for two scores in a 27-second span early in the final period, aided by the gutsy play of a backup cornerback.
Kyle Fuller made two late interceptions for the depleted Chicago secondary, and the first set up the go-ahead score.
"Just coming in here, working hard, it was a team win," said Fuller, the Bears' first-round pick in this year's draft. "We are thankful for that and will keep on building."
Kaepernick threw three interceptions in all, lost a fumble and his cool, a far cry from his breakout start on the Monday night stage nearly two years ago in a rout of the Bears. Cutler sat out that night with a concussion.
A sloppy game filled with 26 penalties - 16 by the Niners - and a crazy collapse overshadowed the fanfare of the regular-season debut for the sparkling $1.2 billion stadium.
The Bears (1-1), in a stretch with six of eight games on the road, go home with some serious momentum despite injuries on both sides of the ball.
Cutler helped the Bears get on the board with a 25-yard run late in the first half. He took a jarring hit from Quinton Dial with 56 seconds remaining, but stayed in the game and threw a 17-yard touchdown pass to Marshall, who made a leaping, one-handed catch to pull the ball into his body as he fell into the end zone.
San Francisco didn't give the ball away once in a season-opening win at Dallas.
The 49ers were embarrassed at home for the second time in a month. They lost 34-0 in a rout by Denver in the first preseason game in the new stadium.
Copyright 2014 by The Associated Press