Romo matched a career-high five interceptions, two of them returned for touchdowns, and was never able to get in tune with his receivers in front of a hugely disappointed Dallas crowd.
"You can have 10 good plays but one play can take away all those things quickly," Romo said. "That's what happened tonight.
"I have to do a better job of maintaining those important plays that win or lose a ball game."
The Bears led by just three points at half-time but took full advantage of Romo's second-half meltdown as Lance Briggs intercepted one of his errant passes and ran 74 yards to give the visitors a 24-7 lead.
"Back in my college days (I played some running back)," said Briggs, a fleet-footed linebacker. "You never know with our team, so you have to get into the endzone somehow."
Cutler fared decidedly better than Romo, tossing two touchdowns in the second half, with the final effort finding Brandon Marshall for a 31-yard completion that put his team 34-10 clear in the fourth quarter.
The Chicago quarterback had suffered a similar fate to Romo against the Green Bay Packers on September 13 when he coughed up four interceptions, was sacked seven times and publicly berated his offensive line.
But Cutler, who completed 18-of-24 passes for 275 yards and no interceptions against the Cowboys (2-2), has rebounded and lifted the Bears (3-1) into a tie with Minnesota for the NFC North lead.
Adding to the good news for Chicago was the return of Pro Bowl running back Matt Forte, who missed last week's game with a sprained right ankle but gained 52 yards on 13 carries.
Marshall had a huge night with 138 yards receiving and a touchdown after he had failed to score in his previous two games.
"Some days it may just be one or two catches (for me), but you have to stay level-headed and stay in the game," Marshall said.
Despite boasting a talented roster, the Cowboys are the lowest scoring team in the NFC this season.
Their running game was once again non-existent and lead rusher DeMarco Murray has managed just 106 yards in his last three games.
With his options limited, Romo was forced to throw often and completed 307 passing yards, including one touchdown, but his game was defined by the interceptions.
- Brandon Marshall