© Getty Images
A very tight first half looked like ending without a single side registering on the scoreboard until Dan Bailey stepped up to convert a 33-yard field goal with 11 seconds remaining to give the Cowboys a three-point lead at the break.
Things brightened up a little in the third quarter when Arian Foster sidestepped one tackle before powering his way into the endzone for a 15-yard touchdown.
Dallas then extended their advantage to 10 points in the fourth quarter as Romo fired a quick pass out left to Dez Bryant, who had a simple catch for a two-yard score.
Randy Bullock pulled three points back for his side with a 29-yard field goal, bringing the Texans within one score with just 2:27 left on the clock.
They managed to find that score with 45 seconds remaining as Foster burst into the endzone from one yard out, while Bullock added the extra point to send the game to overtime.
Houston could not complete the comeback in the additional period, however, as Bailey converted a 49-yard kick to seal a dramatic victory.