After carding a career-low 62 on Thursday - while gaining nearly four strokes putting - Koepka lost over four strokes on the greens in the second round en route to a 1-over 71.
"I just putted bad," Koepka said afterward. "It wasn't really anything other than that. Felt stress-free other than just missing some short ones. On the back nine they felt good, they were just missing. And on the front, they just weren't good putts."
The defending champion missed eight putts from within 15 feet and had a costly three-putt from under four feet that led to a double-bogey. He enters the weekend four shots behind Todd in a tie for third.
Contrastingly, the new leader had a remarkable day on the greens to fire a 5-under 65 and lead the field in putting through two rounds. Todd recently topped the leaderboard after 54 holes at the Travelers Championship but was unable to hold on for his third victory of the season.
Rickie Fowler birdied his final two holes - including a chip-in effort on No. 18 - to grab sole possession of second. He's two back of Todd at 9-under par.
Here's how the leaderboard in Memphis stands after Round 2:
|Place||Player||To Par||R2 Score|
|T3||Byeong Hun An||-7||65|
Threesomes will tee off Round 3 from Nos. 1 and 10 on Saturday due to anticipated inclement weather near TPC Southwind. Tee times will span from 11 a.m. to 1 p.m. ET.