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HOUSTON -- The Dallas Cowboys can breathe a little easier -- and even smile again.

At least for now.

Tony Romo threw two touchdown passes to Roy E. Williams, Marion Barber ran for another score, and the Cowboys got their first win by beating the Houston Texans 27-13 on Sunday.

Romo went 23 for 30 for 284 yards, Williams caught five passes for 117 yards and the Cowboys (1-2) finally put together a complete performance after starting 0-2 for the first time since 2001.

Owner Jerry Jones feared the prospect of a humiliating 0-3 start, and having an extra week to stew over it before his team hosts Tennessee on Oct. 10.

"We were going to really be in bad trouble had we lost this ballgame," Jones said. "Candidly, I was worried about going home and facing five weeks without a win. First five weeks in the NFL without a win; there are all kinds of horror stories."

Coach Wade Phillips said he was losing sleep over the Cowboys' bad start, although Jones said last week that Phillips' job was safe. Now, Dallas heads into an early bye with a victory to build on rather than concerns about what changes the team's unpredictable owner might want to make.

"The thing about this league is you either feel good or feel bad after Sunday," Phillips said. "We feel good right now. Our team came out and showed the way we can play. The little things that were missing in the first couple of games, I think we came through with. We played solid all the way around."

The announced crowd was 71,456, a record for a Texans game at Reliant Stadium. Dallas supporters were well-represented and taunted the hometown fans with "Let's Go, Cowboys!" chant in the waning minutes. The Cowboys became the second NFL team since the merger to reach 400 wins, joining the Pittsburgh Steelers.

The Texans (2-1) blew their chance to not only go 3-0 for the first time, but to gain a foothold in their own state, where the Cowboys have always hogged the attention from the fans and media.

"The guys are upset," star receiver Andre Johnson said. "I wouldn't say that we are down. The guys came in after the game and felt that we played not to our ability. We knew we didn't play our best football."

The Cowboys' defense emerged after two dull efforts, getting its first three takeaways and holding Houston's top-ranked offense to 340 yards. DeMarcus Ware sacked Matt Schaub three times, and the Dallas secondary limited Johnson to four catches for 64 yards.

Ware set the tone on Houston's first series, surging past left tackle Rashad Butler and sacking Schaub. Butler, a five-year veteran, was making his first career start in place of Duane Brown, who began serving a four-game suspension for violating the NFL's banned substance policy. Brown started the last 34 games.

The Texans led 3-0 when Romo threw a 32-yard pass to Felix Jones early in the second quarter. It was negated by an illegal block, exactly the kind of mental error that plagued Dallas in its first two games.

The Cowboys didn't let mistakes slow them down after that.

Williams and Dez Bryant caught third-down passes from Romo to get Dallas moving. Miles Austin beat Brice McCain on a 17-yard reception to the Texans 1, and Barber scored on the next play, the Cowboys' first touchdown rushing this season.

Buehler put Dallas up 10-3 with a 49-yard field goal; he missed shorter attempts in each of the first two games.

Johnson, who sprained his right ankle in last week's win over Washington, aggravated the injury early in the third quarter. Trainers helped Johnson hobble off the field, but he returned for Houston's next series. Schaub threw a deep pass to him that Mike Jenkins intercepted at the 10-yard line for the Cowboys' first takeaway of the season.

Johnson said his ankle nagged him during the game, but didn't limit his movement.

"If I couldn't make plays, I wouldn't go out there," he said. "I felt comfortable going out there and playing on it. It just bothered me."

Romo continued to work on the Texans' suspect secondary, which allowed more than 400 yards passing in each of the first two games. Bryant caught a 30-yard pass down the sideline, and one play later, Williams pulled down a 15-yard touchdown catch over McCain for a 17-3 lead.

Houston rallied from 17 points down to win at Washington last week, and seemed poised for another comeback when it reached the Dallas 1. But the Cowboys twice stopped Arian Foster at the line, and Keith Brooking sacked Schaub on third down.

Soon after, Romo threw a quick slant to Williams, who darted past rookie cornerback Kareem Jackson and sprinted for a 63-yard touchdown. Buehler tacked on a 40-yard field goal for a 27-6 lead with 3:36 left.

"There's no sense of relief," Romo said. "We're still in a position where we've got to keep grinding to get out of this and we understand that. We know that it's not always going to be perfect, but we've got to find a way to keep getting wins."

Game notes

Schaub threw a 7-yard TD pass to Kevin Walter with 1:15 remaining. Before that, the Texans were in danger of failing to score a touchdown for the first time since a 34-6 loss to Dallas in 2006, a span of 61 games. ... Williams had his highest yards receiving total in 28 games with the Cowboys. ... Foster was the first back to top 100 yards rushing against Dallas in 20 games, getting 106. ... Texans S Bernard Pollard made a career-high 15 tackles.