Graeme McDowell moved up the leaderboard following a bogey-free 69 at the the Valero Texas Open, however, the 2010 US Open champion remains ten shots off the lead of Matt Wallace and Jordan Spieth.
McDowell had his best round of the tournament on Saturday to improve to equal-26th overall heading into the final round.
Starting on the back nine, the 41-year-old opened with eight pars before turning with a birdie on the 18th hole.
That brought McDowell under par and two more birdies on the third and seventh holes leaves the Portrush native on two under for the tournament.
Meanwhile, some spectacular putting lifted Ryder Cup hopeful Wallace to a share of the lead with three-time major winner Spieth.
After a slow front nine, Wallace was locked in with his putter down the stretch, birdying three of his final four holes from lengthy distances to close out Saturday at 12 under alongside the American.
Spieth also left it until late to make a move, picking up four shots in his last five holes to match Wallace's score of five under 67.
The pair sit two shots clear of America's Charley Hoffman, who continued his rampage up the leaderboard with a stellar third round score of 65, highlighted by an eagle on the par five 14th.
Overnight leader Cameron Tringale dropped back to fourth after carding a one-over 73 while, Padraig Harrington shot a second consecutive 74 to move back to two over and a tie for 60th place.