World number 102 Schwab, who has posted nine top-10 finishes this season without securing a win, fired a six-under-par third round of 66 to reach 18 under par overall.
He leads a group of five players, including former Masters champion Patrick Reed, by three strokes.
“I’ll just try and do the same stuff that I’ve been doing the last few days, and I’m sure pars will not be enough tomorrow because it’s usually pretty gettable out here,” he said.
An eagle on the opening hole for the second straight day got the 24-year-old off to a flying start.
Despite a double-bogey on the 12th, he made two further birdies, including on the final green, to take control of the tournament.
Reed is level with Scotland’s Robert MacIntyre, Ross Fisher, Frenchman Benjamin Hebert and Ryder Cup winner Tyrrell Hatton on 15-under.
American Reed, who was named as a wildcard by Tiger Woods for next month’s Presidents Cup on Friday, poured in eight birdies.
“At the end of the day, whoever is in the lead, they are in the driver’s seat obviously,” he said. “If they go out and continue playing good golf and make a lot of birdies, going to be hard to catch.”