Looking to win a sixth cap at Medinah next month, Garcia currently lies 11th in the points race after being overtaken by Ian Poulter at the US PGA Championship.
But five birdies, blemished slightly by only his second bogey of the week at Sedgefield Country Club, saw Garcia sign for a 66 and move to 14 under par.
That put the 32 year old one ahead of Bud Cauley and Tim Clark, and victory would put Garcia in an automatic qualifying position ahead of next week’s final qualifying event at Gleneagles.
Another player hoping to make José María Olazábal’s team, Belgian Nicolas Colsaerts, is in a share of 17th place alongside Charl Schwartzel on nine under par.
Garcia said: "Obviously I would love to be two, three shots better but I'm in a good situation.
"It's going to be a tough day, there's no doubt about it. A lot of very good players behind me are trying to achieve the same thing I'm trying to achieve.
"Hopefully I'll go out there in the final round, play well again and give myself a good shot at winning."
"It's going to be a tough day, there's no doubt about it. A lot of very good players behind me are trying to achieve the same thing I'm trying to achieve.
"Hopefully I'll go out there in the final round, play well again and give myself a good shot at winning."
