The Irishman carded a course-record 10-under-par 61, the lowest round of his career, on the frist day but followed up with a two-over-par 73. That left the three-times major winner in joint second spot, two adrift of Americans Dufner and William McGirt.
Dufner had a second successive blemish-free round of 66 and his compatriot McGirt added a 68 to his opening-day 66.
England’s Luke Donald was one of five players tied for fourth spot on seven under par.
Sergio Garcia was in the group on six under after his second consecutive 68, while Justin Rose is one shot further back after a 70.
n World No.1 Yani Tseng went out on her own at the top of the LPGA Founders Cup leaderboard as a round of 70 left her nine under par. IK Kim, Meena Lee and Choi Na-yeon of South Korea were all eight under, along with Ai Miyazato and Mika Miyazato of Japan.