Spieth's one-over par 73 for three-under 213 easily bettered playing partner McIlroy, who struggled to a five-over 77 without a birdie on his card for the first time in 80 rounds at majors.
Unless he can produce a very special final round, McIlroy will have to wait to win the career grand slam, while 22-year-old Spieth is still well-placed to win his third major, leading by a shot despite finishing bogey-double bogey.
"It wasn't ideal having climbed back nicely to get to two-under for the day, I just got really wayward," Spieth admitted.
His closest rival is 24-year-old fellow American Smylie Kaufman, who produced a best-of-the-day 69 for two-under 214.
Kaufman, who already has a victory on the PGA Tour after graduating from Louisiana State, will be paired with Spieth as he contemplates winning his first major.
"An opportunity to win the Masters, it's awesome, what I worked for as a kid," he told Sky Sports.
The next nearest challenger is fully 34 years older than Kaufman, former two-time winner Bernhard Langer from Germany.
The 58-year-old, a dominant force on the Champions Tour, belied his age with a stunning performance, highlighted by three birdies in a row to the 15th.
Only a bogey five on the final hole prevented Langer from being tied for second and the chance to play with the leader in the final pairing.
"It can happen in the game of golf. There are not many other sports it could happen, but in this sport a lot of things are possible," he told BBC Sport.
Langer was later joined on one-under by Hideki Matsuyama of Japan, who might have taken closer order but for successive three putts to undermine his challenge.
Three men, world number one Jason Day, who was paired on day three with Langer, American big-hitter Dustin Johnson and England's Danny Willett are bracketed on level par, three back.
Spieth's late slump would have given them all hope that he can be overhauled, having reached six-under with a birdie on the 15th.
His driving from the tee had been wayward all day, but, in contrast to McIlroy, the Texan scrambled superbly and holed crucial putts.
But his luck ran out on the 17th, where he could only play out from the trees and could not get down in two from short of the green.
Worse was to follow on the tough final hole, driving into trouble on the right.
A good recovery left him the chance to retrieve the situation, but his approach left him in three-putt territory and he eventually pulled a 12-foot par putt wide.
McIlroy missed one final chance to make a birdie after a fine approach to the 18th, closing on two-over 218.
A double bogey after finding the water on the 11th was the low point of his round and he failed to make birdies on the par-five 13th and 15th holes.
Spieth also double bogeyed the 11th, but hit back with birdies on the 12th, 13th and 15th until his late slump.