Justin Rose, introduced for the first time as U.S. Open champion, settled for a 67 and a tie for 18th place during a day of very low scoring at the TPC-River Highlands course.
Hoffman has won twice on the PGA Tour, his most recent victory coming during the 2010 FedEx Cup playoffs at the Deutsche Bank Championship.
He made the turn in 2-under Thursday, then recorded three birdies and two eagles on the final nine holes.
John Daly, who has survived the 36-hole cut in just four of his 10 appearances on the tour this year, shot a 68 that put him in a tie for 34th.
Hoffman has been on the edge of contention in his two most recent starts, but poor fourth rounds have knocked him back in the pack. He shot an 81 at The Memorial to wind up tied for 63rd and then had a 79 to finish the U.S. Open in a tie for 45th.
There were 65 sub-par rounds shot Thursday.
Rose, who won by two last week at the Merion Golf Club for his first major title, bogeyed three out of four holes beginning at the third. He fought back, however, with four birdies in a five-hole stretch on the back nine.