The American carded a 65 on day three to get to 15 under but countryman Reed and South African Van Rooyen were just one back after an enthralling third day in Mexico City.
Rahm's round - his lowest as a professional, a new course record and the joint lowest round in WGC history - contained a stunning hole-in-one on the 17th, the second of the day after Chez Reavie had earlier aced the third.
His 11 under total looked like it would still leave the Spaniard a mountain to climb as Thomas made five birdies on the back nine, but he and Reed both bogeyed the last to leave the door ajar.
Reed and Van Rooyen both carded rounds of 67, while McIlroy signed for a 68 and DeChambeau - who had led by three at one point - bogeyed three of his last six holes in a 71.
Thomas already has a World Golf Championships title to his name and has every right to feel confident going into round four, having finished in the top ten all three times this event has been held at Chapultepec.
"I'll just go out and play golf and keep doing what we're doing," he said. "For the most part I feel like I'm playing well, doing all the right things.
"It's just my bogeys this week have been sloppy, so I'd really like to have a clean card tomorrow and not have any of those and just give ourselves a good chance the last couple of holes."
Reed won this event six years ago in Florida and much like Thomas, he is looking to make small improvements as he goes in search of a first European Tour victory since his Masters Tournament triumph in 2018.
"It was a little sloppy today," he said. "The good thing is I was able to get it around the golf course, get it in the right spots to give myself a chance for birdie.
"Just tighten it up a little bit more tomorrow and the great thing is I'm in good position going into tomorrow, that's all I can ask for."
Van Rooyen won his first European Tour title last season to finish tenth on the Race to Dubai Rankings Presented by Rolex but this is his first time in the final group of a WGC, although he insists the occasion will not get to him.
"You've just got to go play golf, man," he said. "You can't overthink this kind of stuff. At the end of the day, there's 18 holes in front of you and you've got to navigate it the best you can.
"I can't control what Justin Thomas does, he's a phenomenal player. I can't control what Patrick Reed does or the guys behind us. Jon Rahm just went out and shot 61 today. Who's to say one of us is going to win? All I know is I'm going to focus on myself and do my thing."
DeChambeau birdied the short first, eagled the par four second after putting his tee shot to six feet, and a seven foot putt on the fifth meant he led by three shots.
He then found the water at the sixth for a double bogey and Thomas was the man to take full advantage.
The 2017 US PGA Championship winner bogeyed the first after a poor tee shot but got up and down on the second, holed from 16 feet on the third and made the most of the par five sixth.
He holed from 12 feet on the tenth and made a two putt birdie on the 11th to share the lead where he was quickly joined by Reed.
The 29-year-old put his tee shot to tap-in range on the third and holed from the fringe on the fifth before hitting a tree branch to bogey the eighth.
An approach to six feet on the tenth was followed by a gain on the 11th and Reed and Thomas went into battle on the back nine.
A 20 foot putt on the 14th put Thomas ahead but Reed birdied the same hole from half the distance before both men made the most of the par five 15th.
A 14 foot putt on the 17th then put Thomas ahead again before both men bogeyed the last.
Van Rooyen joined DeChambeau in making a birdie-eagle start but he dropped shots on the fifth and seventh after hitting trees.
He made the most of the 11th before putting an approach to three feet at the 12th and, while a poor chip saw him bogey the next, he made a fourth chip-in of the week on the 14th and capitalised on the 15th.
DeChambeau birdied the 12th but then dropped shots on the 13th, 14th and 17th, while McIlroy made five birdies and two bogeys.
Rahm birdied six of his first seven holes and while he bogeyed the eighth after a three putt, gains on the tenth, 13th and 15th followed before his one bounce ace.