The Cowboys were forced to come from behind twice against the struggling Vikings, eventually sealing the victory with just 35 seconds left when Romo threw a seven-yard touchdown pass to Dwayne Harris.
Despite the late nature of the win, Romo insists that he always had confidence in his side due to their ability to keep on fighting until the end.
"We just have to keep the belief throughout the whole football game. I never doubted that we would find a way to win this game, and we did it," Romo told The AP.
The Cowboys remain top of the NFC East with a 5-4 record ahead of next Monday's match against the New Orleans Saints.