After forcing the Falcons into a quick three-and-out, stand-in QB Brandon Weeden guided Dallas down the field again before Randle bundled over from a yard out as the hosts threatened to run away with proceedings early on.
However, Atlanta bounced back with Devonta Freeman finding good blocking in front of him before running into the endzone for a three-yard TD.
Dallas managed to restore their two-score lead with Darren McFadden grabbing the Cowboys' third rushing touchdown of the half.
Before the two-minute warning, the Falcons scored their second touchdown of the day as Freeman danced through Cowboys coverage to cross the threshold.
However, Randle completed a hat-trick of first-half TDs with a one-yard run before Matt Bryant kicked the only field goal to bring Atlanta to within 11.