The 38-year-old sank 10 birdies but bogeys on the 10th and 15th prevented him building a bigger advantage.
Compatriot Jamie Lovemark is in second place after shooting a round of 65.
Five-time major winner Phil Mickleson, also American, climbed the leaderboard with a 66 and trails Dufner by six.
Scotland's Martin Laird made the cut after a 69 moved him to 10 under par but England's Luke Donald (71) missed out.
American Jason Dufner heads into the final round of the CareerBuilder Challenge with a two-shot lead after carding an eight-under-par 64 in California.