McIlroy edged past Open champion Zach Johnson on the 18th to set up a quarter-final with American Chris Kirk, but Spieth lost 4 and 2 in the last 16 to South Africa's Louis Oosthuizen at Austin Country Club.
And that means Australia's Jason Day can replace Spieth at the top of the world rankings with victory over Brooks Koepka in their quarter-final after the pair enjoyed wins over Brandt Snedeker and Matt Kuchar respectively.
McIlroy, who lost the opening hole after duffing a chip, bounced back to win the next two holes before a par on the fourth was enough for Johnson to get back on level terms.
A par on the eighth edged McIlroy back in front but he three-putted the 10th and then saw Johnson hole from 35 feet on the 11th for birdie and save par on the 12th after finding water with his approach.
However, Johnson then made a mess of the 13th and 15th and although he won the 16th with a birdie and holed from 20 feet for another on the last, McIlroy's superb approach had left him just three feet for birdie to seal victory.
Spieth's bogey on the fourth saw him trail in a match for the first time this week and the Masters and US Open champion rarely threatened to get the better of 2010 Open winner Oosthuizen.
After following Spieth into the water on the 11th, Oosthuizen pitched to within inches of the hole to salvage a bogey and win the hole, before birdies on the 12th and 13th set him on course for a quarter-final with Dustin Johnson, who beat Patrick Reed 3 and 2.
Day finished his 3 and 2 victory over Snedeker in style with an eagle from six feet on the 16th, while Koepka held off a figthback from Kuchar to win by matching his opponent's birdie on the last.
Spain's Rafael Cabrera-Bello had been the first player into the quarter-finals by defeating Korea's Byeong Hun An, a win which also sealed a Masters debut next month.
An inspired Cabrera-Bello was about to move five up with six to play when An signalled on the 12th green that a neck injury meant he was unable to continue their last-16 tie.
And that meant the Spaniard - who faces Ryan Moore in the last eight - was assured of winning enough world ranking points to move inside the top 50 in time for the final qualifying deadline for the year's first major championship on Monday.
"Obviously I'm very pleased," Cabrera-Bello told Sky Sports. "It was the only major I had not played before and it's the one that really got me dreaming about being a professional thanks to Olly (Jose Maria Olazabal) winning there twice.
"I'm still concentrating on this week, there is a lot of golf to be played, but I am really, really excited about the Masters."
Spieth had not been taken past the 16th in any of his three group wins, but admitted he feared the worst against Oosthuizen after struggling with his game on the range.
"I didn't make it very hard on Louis today, which is unfortunate," Spieth told reporters. "I was off from when I hit my first 10 shots on the range. The ball was slicing off, which is very odd. I've had incredible control of the ball this week and of my wedges. I'm not exactly sure what happened, I still don't really know.