Si Woo Kim saw his lead at the Valero Texas Open cut to one shot as Corey Conners applied the pressure in San Antonio.
Kim came into the day with a four-stroke advantage but needed a birdie on the 18th, his fourth of the round, to stay in front after Conners carded a six-under-par 66 to move to 14 under par.
Padraig Harrington made the half-way cut, but was eliminated after 56 holes following a one over par third round 73.
He hit four bridies, three bogeys and a double bogey on the par four fifth. He packed his bags along with the other players who sat on even par on Saturday evening.
Conners started his round brilliantly, picking up five shots in the first seven holes and almost producing an ace on the par-three third.
The Canadian sits one shot clear of Charley Hoffman, who saved the best until last in his 64 as he eagled the 18th following a 284-yard approach shot.
Scott Brown and Jhonattan Vegas both carded 67s to sit in a tie for fourth alongside Kyoung-Hoon Lee, four shots off the lead.
However, others suffered on day three, with former world number one Jordan Spieth and Rickie Fowler each carding 73s to tumble from a share of second place to a share of 14th.
Spieth did well to manage that, firing five birdies on the back nine to recover from an awful first half of his round.
Similarly, Fowler produced an eagle on the 18th to finish the day on seven under.