Masters champion Bubba Watson birdied the par-3 17th to get to 2-under 142, the number he needed to survive the 36-hole cut.
Dufner has never won on the PGA Tour, but he has given himself lots of chances in the past year. He fell victim to a late comeback by Keegan Bradley at last season's PGA Championship and then lost to Bradley in a playoff. He led the Phoenix Open this year after an opening-round 66 and wound up tied for eighth, and his first two rounds of 66-66 put him in front at the Transitions Championship, but he faded on the weekend and finished in a tie for 10th.
At the Masters, he shared the 36-hole lead with Fred Couples only to end the tournament tied for 24th. He was a shot out of the lead at the halfway mark of the Arnold Palmer Invitational before finishing tied for 15th.
The third round will begin with 21 players within five shots of the lead.
Camilo Villegas, Cameron Tringale and Graham DeLaet shared eighth place at 135 while Rickie Fowler was among those at 136. Ben Curtis, the winner last week in San Antonio, was in the large group at 137.
Former British Open champ David Duval made his second straight cut at 141 after missing the cut in his first seven tournaments of the year. John Daly, given a late sponsor's exemption to play in the event, had two double bogeys and a triple bogey in a round of 80 and he missed the cut by 11 shots.