The Cowboys expanded their lead on a 33-yard field goal by Dan Bailey with 40 seconds left in the quarter.
Ahmad Bradshaw’s 10-yard touchdown run brought Giants within 14-10 late in the third quarter.
The key play on the drive was a spectacular leaping grab by Domenik Hixon in traffic, a 39-yard play to the Cowboys 10.
The Cowboys scored on their final drive of the first half. Romo found Dez Bryant streaking down the right side for a 38-yard gain that moved the ball to the Giants 15. Two plays later, Romo lofted the scoring pass to Ogletree with 1:01 left in the half.
Earlier in the quarter, Michael Boley’s 51-yard interception return set up a 22-yard field goal by Lawrence Tynes as the Giants opened the scoring. Boley returned the pick of Romo to the Cowboys 2 and a horse-collar penalty gave New York a first-and-goal from the 1. The Giants lost ground on two runs by Bradshaw and a third-down pass to the end zone failed.
Tynes kicked the field goal with 9:10 remaining.
In the first quarter, the Giants kept the Cowboys off the board with a strong defensive stand. Facing a fourth-and-inches from the Giants 37, the Cowboys went for it and came up short when Lawrence Vickers was stopped for no gain.
Cowboys starting center Phil Costa aggravated a back injury that kept him out of most of the preseason. He was replaced by Ryan Cook.
Giants cornerback Michael Coe left the game with hamstring injury.