2011 winner McIlroy - who has not won a major since 2014 - and defending champion DeChambeau head into Sunday on three under par, just two shots off the leaders.
There is currently a three-way tie for the outright lead at Torrey Pines, with Mackenzie Hughes, Russell Henley and Louis Oosthuizen all level on five-under for the tournament.
Former Open champion Oosthuizen holed from 50 feet for an eagle on the 18th in his 70, while Hughes carded a 68 and halfway joint-leader Henley returned a 71.
McIlroy covered his first 10 holes in two under par and, although he missed a good chance on the 11th, the former world no1 made amends in style, chipping in from short of the green for an unlikely gain on the next.
The 32-year-old then amazingly hit the pin with his approach to the 13th from 260 yards, but did well to two-putt from long range for birdie, only to then pull his drive on the 15th into a ravine.
Following a penalty drop, McIlroy was still left with 240 yards to the green and came up short with his third shot, but hit a superb pitch to five feet and holed the putt to limit the damage.
After saving par from a greenside bunker on the 16th, McIlroy parred the 17th and then birdied the par-five 18th to boost his chances of ending his frustrating major drought.
Asked about the prospect of winning another major on the 10th anniversary of his maiden victory, McIlroy told Sky Sports: "It would mean an awful lot. I am just so happy that I've given myself another chance.
"It feels like a while since I've had a chance to win a major championship going into a Sunday and it was great to play a round of golf today to give myself that chance.
"It's not going to be quite as easy as it was 10 years ago, but my game feels good and a round like today proves I can go out there again and try to do the same thing tomorrow."
DeChambeau is alongside McIlroy on three under following a 68, with pre-tournament favourite Jon Rahm, Scottie Scheffler and Matthew Wolff another stoke adrift.
World no1 Dustin Johnson is part of a five-strong group on one under, with Paul Casey, Ian Poulter, Francesco Molinari, Justin Thomas and Brooks Koepka all on level par.
"Conditions were perfect for golf, slightly overcast, slight little wind," Casey told Sky Sports after his 67.
"I don't think the course is any different (from the first two days). I think we've seen today some more accessible pin positions, a couple of tees have been moved up.
"I drove it brilliantly the first two days and didn't really capitalise on how I struck it. I didn't have the speed down with the putter and today was the first day where I felt like I had touch on these greens."
England's Richard Bland held a share of the halfway lead but struggled to a 77 on Saturday to fall six shots off the pace.
Additional reporting by the Press Association.