Though Romo was only sacked once, on the Cowboys' opening series, he was pressured relentlessly and threw five interceptions. That matched his career high, set five years ago in his first full season as a starter.
"Just outstanding play by our defense," Bears coach Lovie Smith said. "Seems like everybody had a say. Those were all good plays."
Briggs' 74-yard interception return came in a wild two-play exchange of turnovers midway through the third quarter.
"I got the ball, I just tried to score," said Briggs, who had not returned a pick for a touchdown since 2005. "I needed to get in the end zone."
Bears quarterback Jay Cutler was nearly flawless after halftime, when he completed 11 of 12 passes for 219 yards and two touchdowns. That included a 34-yard score to Devin Hester to start the half and a 31-yarder to Brandon Marshall with 6Â½ minutes left.
Cutler was 18 of 24 overall for 275 yards. Marshall had seven catches for 138 yards.
Major Wright, who returned an interception for a touchdown in Chicago's last game, had two of the five interceptions. D.J. Moore has nine career interceptions, three of them against Romo after getting another one Monday night.
On the very next play, Romo was trying to escape pressure when he was hit from behind by Henry Melton. The ball popped forward into the air and Briggs grabbed it and rumbled for his first interception return for a score since 2005 to put the Bears (3-1) ahead 24-7.
Once again, the Cowboys (2-2) are a .500 team. They are also one of the lowest-scoring team in the NFL with only 65 points.
Since the start of the 1997 season, Dallas is 122-122 in regular-season games. They have won only one playoff game in that span after three Super Bowl titles in a four-year span in the first half of the 1990s.
Romo finished 31 of 43 for 307 yards and a touchdown. When the Cowboys got the ball back in the final 3 minutes, Kyle Orton got his first action since the veteran quarterback signed a free agent deal during the offseason to be Romo's backup.
The regular referees were back, wrapping up the first weekend of games since returning to work. It was a week after that disputed Monday night ending that gave the Seattle Seahawks a victory over the Green Bay Packers.
Chicago opened the second half with a 73-yard drive capped by Cutler's 34-yard TD pass to Hester, who raced passed rookie cornerback Morris Claiborne and had to make a lunging catch at the goal line.
Despite a screen shot frozen on the huge video board over the field that raised the question of whether the ball might have hit the ground as Hester rolled over, Anderson confirmed the on-field ruling of touchdown after reviewing the play.
There was another play involving Claiborne overturned on review later in the third quarter. When Alshon Jeffery was going down after a catch, Claiborne stripped the ball and started running the other way. It was originally ruled a fumble, but the replay showed the receiver still controlled the ball when his elbow hit the ground.
In the fourth quarter, Dallas challenged a pass interference call against its defense in the end zone. They contended that the ball had been tipped, which was confirmed by replay.
That brought up fourth down, and Robbie Gould kicked his second field goal, a 21-yarder.
The interception by Tillman in the second quarter, on a ball thrown right into his hands by Romo when intended receiver Dez Bryant was still running down the field, came on the third play after Gould's 43-yard field goal.
Dallas responded to that quick 10-point surge by going 80 yards on nine plays, capped by Romo's 10-yard TD pass to Miles Austin with 14 seconds left in the half.
The Bears had an NFL-high 14 sacks through the first three weeks of the season, and quickly upped that total. Melton, from nearby Grapevine and a former University of Texas running back, sacked Romo on third-and-7 from the Bears 40.
Witten, the seven-time Pro Bowl tight end who uncharacteristically had several drops the first three games after missing most of the preseason with a lacerated spleen, had 13 catches for 112 yards. Bryant had eight catches for 105 yards.
Copyright 2012 by The Associated Press