Then, when the 34-year-old quarterback playing with a surgically repaired back made another off-balance throw under pressure in overtime, Dez Bryant's spectacular catch saved the Dallas Cowboys from a late meltdown.
"Just got to come down with it, come down with it," said Bryant, who had game highs with nine catches and 85 yards. "That's something I always tell Tony. If the ball is in the air, I'm going to try my best to come down with it."
After the Texans scored twice in the last 2:27 of regulation, Bailey's miss from 53 yards on the final play ended a franchise record streak of 30 straight made field goals.
"We had to go down and basically win the game twice," said Romo, who threw for 324 yards with two touchdowns with an interception that took away a scoring chance in the fourth quarter. "You just put your work hat on and go out and execute."
The Cowboys (4-1) won their fourth straight for the first time since 2011 heading into a trip to Super Bowl champion Seattle, their only road game in a stretch of six games.
The Texans (3-2) rallied behind Arian Foster, who had 157 yards rushing and a tying 1-yard score with 41 seconds left in regulation.
"Football is a brutal game," Watt said. "It's brutal on your body. It's brutal on your emotions. To fight back the way we did, to show that resilience, it was good to see. But at the end of the day, we lost the game."
NFL rushing leader DeMarco Murray had 136 yards for Dallas, his fifth straight 100-yard game to start the season.
After the Cowboys stopped the Texans on the first possession of overtime, they were facing third-and-8. Romo unloaded off his back foot to avoid a sack. Bryant reached over Johnathan Joseph on a 37-yard gain to the Houston 31. Bailey's kick came three plays later.
"Dez, I've seen him make it a million times," said Jason Witten, who became the third tight end in NFL history with 10,000 career yards receiving. "I don't know that there's two better people at clutch moments than Tony and him."
The Texans pulled even by converting a fourth down on a drive to Randy Bullock's 29-yard field, then got the ball back in just 32 seconds. They went 45 yards in four plays to Foster's second touchdown with 41 seconds left.
Houston had just 86 yards total offense at halftime, but Foster had 117 rushing himself in the second half. He went 48 yards on consecutive plays, the latter from 15 to put Houston ahead 7-3 in the third quarter.
Romo answered four plays later on probably the best test so far of his back after surgery last December to repair a herniated disk.
He spun to his right as Watt closed in, then threw about as far as he could with more pressure coming. Terrance Williams had an easy 43-yard catch in the end zone when Houston's Kendrick Lewis fell at the goal line just before the ball arrived.
"Certainly it's one for the ages with Romo," coach Jason Garrett said. "There's a handful of those he's had throughout his career, and I think you can add that one to the list."
Witten helped set up Williams' score with a 34-yard catch to join Tony Gonzalez and Shannon Sharpe as the only tight ends with 10,000 career yards receiving. He finished with 59 yards to put him at 10,014.
Murray, who had his fourth fumble in five games in the first quarter, was denied a chance to join Jim Brown and O.J. Simpson as the only running backs with at least 100 yards and one touchdown in the first five games of the season.
It looked like he would get the TD, but Romo instead threw a 2-yard scoring pass to Bryant for a 17-7 lead in the fourth quarter.
Texans WR Andre Johnson became the second-faster receiver to 950 catches by finishing with five for 954 after 159 games. He'll have to wait at least another week to be the second fastest to 13,000 yards, finishing with 58 to fall 19 yards short. He has two more games to beat Marvin Harrison's mark of 162 games. Jerry Rice did it in 154. ... Murray set a Dallas' franchise record with his fifth straight 100-yard game to start the season. Emmitt Smith had four in 1995.