Webb Simpson shot a three-under-par 67 on Saturday to break out of a crowd and take the third-round lead at Colonial.
But Paul Casey holed a 23-foot putt on the 18th to leave himself within two shots of the lead at the Dean & DeLuca Invitational.
England's Casey, who is without a win on the PGA Tour since 2009, goes into the final day behind only Simpson after recording a two-under-par 68 in the third round in Texas.
Casey is joined on seven under par by New Zealand's Danny Lee, while American duo Stewart Cink and Kevin Kisner are both one shot further back.
Defending champion Jordan Spieth is five shots off the lead on four under, as is Masters champion Sergio Garcia, who had three bogeys in a one-over 71.
Casey started the third round one shot behind four co-leaders and reached the turn in 36 following a dropped shot on the eighth but began the back nine with successive birdies.
Another bogey on the 12th threatened to stall his progress but he responded by sending his tee shot to within four feet at the par-three 13th for a birdie, before his superb putt on the last left him right in contention for a win on Sunday.
Simpson, the 2012 US Open champion, dropped his only shot of the day on the eighth but birdies on the first, second, 10th and 11th saw him sign for a three-under 67.
Lee, who shot the week's lowest score on Friday, kept in touch with a 69. He had three birdies and three bogeys in his first eight holes, before recording nine successive pars and then draining a 16-foot putt on the last for birdie.
Northern Ireland's Graeme McDowell slipped back on day three, as a two-over 72 left him seven shots off the pace.