Romo completed 36-of-49 pass attempts with an interception in the season-opening victory for Dallas (1-0) after bouncing back from a hard hit near the end of the first half.
On the play, Giants pass rushers Mathias Kiwanuka and Justin Trattou hit the signal-caller simultaneously. Romo stayed down on the field in pain for several minutes before limping off the field, but returned in the second half to finish off the game.
The Cowboys' 13-point lead was whittled to six at 30-24 after Eli Manning hit Victor Cruz with a 10-yard TD pass with 8:54 left in the game, but Dallas' Brandon Carr iced the win with a 49-yard interception return for a touchdown.
Manning went 27-of-42 for 450 passing yards and four touchdowns but was intercepted three times as New York (0-1) committed six turnovers in all.
Cruz finished with three TDs on five catches for 118 yards, while Hakeem Nicks and Rueben Randall combined to gain 215 yards on 10 receptions for New York.