Romo threw for two TDs in the third quarter. But the Giants (3-8), trailing 24-21, staged a 93-yard drive capped by Adrien Robinson's first career TD catch, from 1 yard with 3 minutes left.
Back came Dallas (8-3) on an 80-yard march in which Romo never was pressured. He found Bryant in the back of the end zone to win it, setting up an NFC East showdown with Philadelphia on Thanksgiving Day for first place.
Thanks to Odell Beckham Jr.'s spectacular one-handed catch, one of the rookie's two first-half touchdowns, New York built a 21-10 halftime lead. But the Giants lost their sixth straight and were eliminated from division contention.