CHICAGO (AP) -- Tony Romo looked desperate early on, scrambling, rushing throws and doing all he could to avoid the Chicago defense. The only thing he didn't do was go away.
It looks like the Cowboys won't, either.
Romo passed for 329 yards after a rough start, Anthony Henry had two interceptions for the second straight week and Dallas made a big statement, beating the Bears 34-10 on Sunday night.
The Cowboys showed just how serious a contender they are in the NFC during the second half, outscoring the Bears 31-7. Dallas is 3-0 for the first time since 1999.
"I think this journey that we're going on has been pretty fun, and I think it's going to be really exciting for the rest of the year," Romo said.
He again showed that last season's rise from obscurity to the Pro Bowl was no fluke, going 22-for-35 with two touchdowns and an interception.
He led the Cowboys on an 89-yard touchdown drive to start the second half, breaking a 3-3 tie. And he put the Cowboys ahead for good, 17-10, with a 10-yard touchdown pass late in the third period that capped a 91-yard drive.
Henry added a 28-yard interception return early in the fourth quarter to make it 27-10, and Marion Barber scored from the 1 after breaking off a 54-yard run.
It was a terrible night all around for the Bears (1-2).
The defending conference champions lost four Pro Bowl players to injuries: linebacker Lance Briggs (groin), cornerback Nathan Vasher (groin), defensive tackle Tommie Harris (knee) and guard Ruben Brown (ankle).
Rex Grossman had another rough outing, going 15-of-32 with 195 yards. He threw three interceptions, did not have a touchdown and was sacked three times -- twice by DeMarcus Ware. That's why Grossman heard more boos from the home crowd.
If he's worried about his job security, Grossman wasn't letting on.
"I'm going about my business and not worrying about the things that I don't control," he said.
Would it surprise him if he lost his job? Grossman said, "Same answer."
Coach Lovie Smith continued to support the embattled QB.
"Rex Grossman is our quarterback," Smith said. "I know he's going to take a lot of the blame. We all will take a lot of the blame. We didn't get a lot done."
Not that Grossman had much help.
Bernard Berrian caught six passes for 73 yards, but dropped a potential touchdown pass in the first half.
Cedric Benson ran for 46 yards on 16 carries, and the Bears could only muster 239 yards against the 25th-ranked defense. They fumbled three times and lost one, and have 11 turnovers in three games.
Brian Urlacher had two sacks, but the Cowboys finished with 431 yards. After scoring a combined 82 points in the first two games, Dallas perked up in the second half to add to its total.
By the time it was over, Terrell Owens had eight catches for 145 yards. He moved past Michael Irvin into 14th place on the NFL's career list with 12,044 yards and became the 14th player to pass the 12,000-yard mark.
Jason Witten caught six passes for 90 yards and Barber ran for 102 yards on 15 attempts.
"I think we're a very explosive offense," Romo said. "The funny thing is last year I think we were a good offense as well, but I was probably more of 67 completion percentage type guy, this year we're going down the field in chunks. And you're not going probably going to have as high completion (percentage) but you're probably going to score more points with the way we're doing things."
Romo, who grew up about 80 miles away in Burlington, Wis., came into the game with a 119.3 rating that ranked second among quarterbacks with two starts behind Tom Brady. But he hadn't faced a defense like Chicago's.
After passing for 17 yards in the first quarter, Romo went to work.
He and Owens led the Cowboys on an 89-yard touchdown drive to start the second half and break a 3-3 tie, hitting Owens with a 23-yard pass and two 18-yarders before Witten's 3-yard scoring catch.
The Bears then drove 86 yards -- 52 of them coming on a pass to Desmond Clark before Benson ran it in from the 1 to tie it.
But Romo connected with Barber for a 10-yard pass with 1:26 left in the third that put Dallas ahead.
Nick Folk kicked a 44-yard field goal just under three minutes into the fourth, and moments later, the Cowboys put away the Bears. Henry stepped in front of a pass intended for Muhsin Muhammad and ran it back 28 yards, making it 27-10.
"I feel like it was mission accomplished coming in here and playing against a great defense," Owens said. "They gave Tony some fits. They bring a heck of pass rush and Tony was able to escape and use his ability to get out of some of those jams and find some open guys down the field.
Briggs appeared to injure himself midway through the second quarter, when Urlacher sacked Romo. Briggs, who was trying to avoid Urlacher, stayed in the game but did not come out for the second half. Vasher, a Pro Bowl pick in 2005, walked off the field midway through the third quarter after being injured away from the ball. Harris and Brown were injured in the fourth. ... Bears rookie TE Greg Olsen caught two passes for 28 yards after missing the first two games with a sprained knee. ... This is Dallas' 14th 3-0 start.