The Cowboys needed the late heroics after the Giants had scored 15 straight points to forge a 21-21 tie.
Romo finished with 250 yards, three TDs and an interception on a 23-of-38 efficiency for Dallas (6-5), which moved into a first-place tie with Philadelphia in the NFC East.
Bryant hauled down nine total passes for 102 yards, Jason Witten made two scoring grabs and safety Jeff Heath returned a fumble for a touchdown.
Eli Manning threw a pair of scoring strikes en route to 174 yards for New York (4-7), but his comeback try faltered at the end.
Andre Brown led the Giants' ground game with 127 yards on 21 carries.