England's Paul Casey (68) and South Korea-born New Zealander Danny Lee (69) are joint second on seven under.
Simpson, the 2012 US Open champion, survived another windy day to post a nine-under 201 total at Colonial Country Club in Fort Worth.
The 31-year-old also saw a 15-foot birdie putt lip out at the final hole.
Americans Stewart Cink (66) and Kevin Kisner (70) are three off the pace, while defending champion Jordan Spieth (68) and Masters champion Sergio Garcia (71) are both five shots behind.
Northern Ireland's Graeme McDowell dropped shots at three consecutive holes on his front nine as he shot a two-over 72 to fall seven strokes adrift.
World number 14 Casey, without a PGA Tour victory since 2009, began the day in a group with Garcia one behind a four-way tie for the lead.
The 39-year-old had three birdies in four holes at the start of the back nine, sending his tee shot to within four feet at the par-three 13th.
After finishing with a 23-foot putt for a birdie at the last, he said: "Weeks I've putted well I've always had a chance to win, or won. We can't predict the future but I'm very excited with how I've been playing."
Former world number one Spieth played the final seven holes with trainer Damon Goddard carrying his bag after regular caddie Michael Greller fell ill in the oppressive heat and humidity.
"Michael went down with heat exhaustion," said Spieth, who finished with two birdies in the last three holes and is in a share of eighth.
"When we were walking down the 11th, he said: 'This is my last hole.' I thought he was acting a little strange, a little quiet."
American Webb Simpson carded a three-under-par 67 to open a two-stroke lead after the third round of the Dean & Deluca Invitational in Texas.