Westwood lost one-down to American Nick Watney in the second round, left-hander Mickelson was stunned 6 and 5 by fellow American Rickie Fowler and Northern Irishman McIlroy was pummelled 8 and 7 by American Ben Crane.
Second seed Martin Kaymer of Germany survived a tight encounter with Britain’s Justin Rose after 20 holes and will next meet American Hunter Mahan, a 2-up winner over Swede Robert Karlsson.
In other matches, long-hitting Bubba Watson hammered fellow American Mark Wilson 6 and 5 while Italian teenager Matteo Manassero continued his remarkable debut at the event with a 1-up win over South African Charl Schwartzel.
In many respects, the premature exit of world No. 1 Westwood did not come as a major surprise as the Englishman had never reached the third round in 11 appearances.
“I think we were pretty even tee to green,” Westwood told reporters at Dove Mountain’s Ritz-Carlton Golf Club after losing a match where he trailed from the very first hole.
“Nick just holed a few more putts than me. But that’s the way match play goes. You have to take your chances.”
Mickelson, who crushed Australian Brendan Jones in Wednesday’s opening round, ran into a human buzzsaw as Fowler recorded five birdies and two eagles, one of them conceded.
“I played great,” the 22-year-old Fowler said after outplaying the four-times major champion. “After making bogey on three, I turned things around with two birdies.
“And Phil left a couple of doors open that I took advantage of. My momentum kind of went my way from there.”
Mickelson, who has been something of a mentor to Fowler since the American turned professional in 2009, applauded his opponent’s form.
“He’s a heck of a player and he played some good golf today,” the world No. 5 said. ” I didn’t quite have my ‘A’ game. I just couldn’t keep pace.”
McIlroy, who reached the last eight on his debut at Dove Mountain two years ago, succumbed to the second-heaviest defeat ever in the elite 64-man event.
Crane, ranked 38th, birdied three of the first six holes to go four up before sealing victory at the par-5 11th where McIlroy pushed his tee shot well right into the desert scrub.
“Rory didn’t have his best day and things were all going in my favor,” Crane said after recording seven birdies, two of them conceded, in 11 holes.
“I got up and down from some crazy spots. I played exceptional today — it was one of the best rounds I’ve ever played.”
Crane’s victory margin of 8 and 7 had previously been achieved twice at the event.
Three-times champion Tiger Woods holds the record for the heaviest win, having hammered Canadian Stephen Ames 9 and 8 in the first round in 2006.
Australian Jason Day pulled off yet another upset in the unpredictable match play format by beating Britain’s Paul Casey 4 and 2.
Casey has reached the final here for the last two years but he was outplayed by Day, who piled up six birdies and one bogey in bright desert sunshine.
US Open champion Graeme McDowell of Northern Ireland beat Englishman Ross Fisher 4 and 2, ensuring he will overtake world NO. 3 Woods in next week’s rankings.
Three-times major winner Ernie Els was upset by big-hitting American J.B. Holmes 1-up, twice champion Geoff Ogilvy of Australia scraped past Denmark’s Thomas Bjorn one up and South Korean Yang Yong-eun beat American Stewart Cink 4 and 3.
