Dufner, the 2013 PGA Championship winner, collected eagles on the par-five second and fifth holes, then struck for birdies at the 14th through 16th holes for a round of six-under 65 at Harbour Town Golf Links on Hilton Head Island.
He settled down after an uneven front nine that featured the two eagles, three bogeys and a birdie to stand at 13-under 200.
DeLaet, who shared the lead with Luke Donald after Friday's play, bogeyed the final hole to miss an opportunity to tie Dufner.
He shot 69 for the day, making four birdies and two bogies.
Donald dropped into a tie for sixth at 204 after a one-over par 72.
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Toby Davis)