ARLINGTON, Texas -- Dak Prescott takes another step with each start, and Sunday was no different.

The rookie threw his first touchdown pass and the Dallas Cowboys pounded the Bears 31-17 at AT&T Stadium.

Dallas improved to 2-1, remaining tied with the New York Giants and one game behind 3-0 Philadelphia in the NFC East.

"We battled well as a team," Dallas coach Jason Garrett said. "Obviously, got off to a good start in the ballgame. We did some good things on offense, made some stops on defense and we knew they were going to battle back."

Prescott had another impressive showing in his third career game and start in place of Tony Romo. The fourth-round pick from Mississippi State completed 19 of 24 passes for 248 yards for a touchdown and ran for another.

Fellow rookie Ezekiel Elliott gashed the Bears for a season-high 140 yards on 30 carries a week after fumbling twice at Washington.

"He's gotten better and better every week," Garrett said. "Made a lot of really good runs, lot of tough runs, NFL runs. He's finishing forward a lot."

Dez Bryant caught his first touchdown pass of the season, a 17-yarder in the fourth, to push Dallas' lead to 31-10. Bryant became the fourth player in franchise history with 60 career touchdowns.

That was also Prescott's first scoring pass. There was some question whether Bryant or Prescott would get that milestone ball.

"If he wants it that bad he can have it," Prescott said. "I plan to get many more."

Dallas finished with a season-high 447 total yards.

The Bears (0-3) weren't as fortunate with Brian Hoyer at the helm.

Pressed into action with starter Jay Cutler's thumb injury, Hoyer didn't do much with the game on the line against a Dallas defensive unit that ranks in the middle of the pack in most statistical categories.

"The bad thing about the first three games is we can't put a complete game tonight," Bears coach John Fox said. "We've been on the road twice, once at home, that's very hard. At this point all I know is that it's not going well. You either give up or give in or just give it your all."

Hoyer was 30 of 48 for 317 yards, with two touchdowns to Zach Miller, but he didn't heat up until the Bears were down by three touchdowns. Hoyer also lost a fumble.

Miller caught eight for 78 yards, with his first touchdown coming on fourth down midway through the third quarter. Alshon Jeffery had five receptions for 70 yards.

Prescott led the Cowboys to points on their first four drives and a 21-point advantage. If not for a fumble by Terrance Williams after a long run after catch in the third quarter, it could have been five for five.

Dallas didn't punt until the 5:20 mark of the third.

The Bears' defensive effort didn't sit well with Fox.

"Anytime you give up 31, it's not good enough," Fox said. "We have to look at that hard."

The Cowboys, at San Francisco next week, snapped an eight-game home losing streak that included the last seven games of 2015.

The Bears return to Chicago searching for their first win against NFC North rival Detroit.

The Cowboys took a commanding 24-3 lead into halftime. They were a picture of balance with nearly a 50-50 split in the passing and rushing yardage in the first half while holding the ball for nearly 22 minutes.

Dallas had 274 yards by the break to Chicago's 114 yards.

The Cowboys steamed down the field on their first possession with ease, with Elliott picking up big chunks of yards and Prescott perfect through the air. Prescott finished the 75-yard drive by powering the ball in from the 1.

Dallas went up 10-0 when Dan Bailey connected on a 49-yard field goal late in the first quarter.

The lead reached 17-0 early in the second quarter on Lance Dunbar's 1-yard run. Prescott dropped in a perfectly placed 29-yard toss to Beasley that came up just short of the goal line.

The Bears got on the board midway through the quarter on Connor Barth's 34-yard field goal.

Alfred Morris put the finishing touches on another long Dallas march with a 3-yard touchdown in the last minute of the first half.

NOTES: Dallas was without LT Tyron Smith (back) and CB Orlando Scandrick (hamstring). Smith's back tightened up Friday and Scandrick didn't practice all week. Other Cowboys inactives: QB Tony Romo, RB Darius Jackson, LB Mark Nzeocha, DE Charles Tapper and S Kavon Frazier. ... Chicago had two active QBs with Jay Cutler (thumb) inactive. Brian Hoyer started and was backed up by Matt Barkley. Other inactives: CB Bryce Callahan, RB Ka'Deem Carey, CB Kyle Fuller, NT Eddie Goldman, C Eric Kush and LB Danny Trevathan. ... Chicago had won the two previous games at AT&T Stadium.