Shane Lowry is the highest placed Irish challenger ahead of Sunday's final round at the WGC-FedEx St Jude Invitational in Memphis.
The Offaly native's 67 leaves him on six under, six shots behind leader Brendon Todd in a tie for 10th.
Lowry's round included five birdies as he picked up three shots on day three.
Graeme McDowell is four shots behind Lowry on two under after a 70, while Rory McIlroy is well off the pace after a 73 left him on two over par.
The world number two had enjoyed a revival on Friday but Saturday's round saw him revert back to the form of his opening day 73, with four bogeys and a single birdie on his 15th hole.
Phil Mickelson made his move in the third round as Rickie Fowler also looked to challenge Todd at the top of the leaderboard.
Mickelson, a five-time Major winner, recovered after dropping a shot at the par-four second to go to the turn three under at TPC Southwind.
After a bogey on the 10th, the veteran American then picked up two more shots heading into the 15th, which put him in a tie for fourth place at seven under.
Fowler, meanwhile, had moved into the lead at 12 under after a three-under-par front nine.
Overnight leader Todd started with a birdie, but dropped a shot at the fifth to turn one under. Another bogey at the par-four 10th saw him fall back to even par for the day and 11-under overall.
South African Louis Oosthuizen was another to move up the leaderboard after picking up two strokes early on the back nine.
Defending champion Brooks Koepka had slipped off the pace after a 71 on Friday, and had with a double-bogey six at the second, dropping another at the sixth as he turned two over.
The American, though, had pulled three shots back heading to the 13th.
South Africa's Christiaan Bezuidenhout hit a six-under 64 to climb up into a tie for seventh, while American Joel Dahmen shot 65 to also finish at six under after three rounds.