Shane Lowry produced a solid third round of 67 at the WGC-FedEx St Jude Invitational in Memphis Tennessee.
The Offaly native currently finds himself tied for 11th after bettering his two previous rounds of 68 and 69 respectively going into the final round on Sunday.
The reigning British Open champion is currently seven shots off the leader Bredon Todd of the USA.
Graeme McDowell, meanwhile, carded a round of 70 to leave him on two-under on Saturday while Rory McIlroy proved to be way off the pace with a forgettable round of 73, leaving the Co Down native on two-over.
Meanwhile, Mickelson made his move on Saturday as Rickie Fowler also looked to challenge Brendon 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.