Northern Irishman McIlroy, a losing finalist last year, was ousted 1-up by his good friend Shane Lowry of Ireland while Woods was eliminated 2&1 by fellow American Charles Howell in fading light at Dove Mountain.
Once again the elite World Golf Championships event lived up to its reputation for wild unpredictability and there were 14 upsets from the 30 matches which finished at the Ritz-Carlton Golf Club.
Two matches will have to be completed on Friday, a knock-on effect from Wednesday when just three-and-a-half hours of play was possible because of driving rain, sleet and then snow.
The premature departure of McIlroy in his first US PGA Tour appearance of the year was stunning, but Lowry always believed he had the game to pull off an upset win.
"Deep down I knew I could beat him," the 25-year-old Irishman said after chipping in for birdie at the 11th and 12th to take control of the match. "I'm not here for no reason. I'm not here to make up the numbers.
"It was a bit of an up-and-down match, and I'm not going to lie, we didn't play our best golf. But that's match play. I'm happy to get the win, and I'm looking forward to tomorrow."
Woods, Match Play champion in 2003, 2004 and 2008, was eliminated at the first hurdle for a third time at the event.
"I played well, I really did," said the world number two. "I hit a lot of good shots out there. I didn't make a bogey out there. Unfortunately it's the nature of the format, and I'm not advancing."
Howell, who has played Woods several times in practice, was delighted to beat the former world number one for the first time.
"I knew I had to play extremely well to have a chance, and I still kept waiting for that Tiger moment," said Howell, who set up the win with birdies at the 15th, where he nearly holed out with a wedge, and the 16th.
"I had nothing to lose coming into this match. Every time Tiger Woods tees it up, he's a marked man and he's got the bulls-eye on his back. It shows you that match play is crazy. I did have to play a good round."
In other upsets, US Tour rookie Russell Henley beat in-form South African Charl Schwartzel 1-up and Spaniard Rafael Cabrera-Bello came from two down with seven holes left to scrape past British world number eight Lee Westwood after 19 holes.
Australian Jason Day, Belgian Nicholas Colsaerts and South African Richard Sterne also delivered upset wins based on the seedings but Henley's triumph initially caught the eye given his opponent's scintillating recent form.
The American rookie, who clinched his maiden US Tour victory at last month's Sony Open, never trailed and held off a late fightback by 2011 Masters champion Schwartzel with pars on the last three holes.
Schwartzel had won twice, sealed two runner-up spots and added three more top-five finishes in his last seven starts worldwide but he struggled against Henley with four bogeys in the first 13 holes.
"I just give it everything I had, tried to hang tough and play until the end," said Henley. "I've heard a lot of comments from people saying they expected him to win, and that gave me a little motivation for sure."
Henley will next meet Day, who completed a crushing 6&5 win over Zach Johnson when the American missed a birdie putt from 14 feet at the 13th in a bid to keep their match alive.
"Everything was good," said Day, who was five under par after 13 holes. "I missed two greens out of the 13 holes that I played, I hit a lot of good quality shots, and I putted great."
Cabrera-Bello, ranked 60th in the world, made three birdies in his last 10 holes and was elated after beating former world number one Westwood.
"It feels very good," the Spaniard said. "I just know really the odds were in his favour, but in match play anything can happen. I just tried my best, and I was fortunate enough to win."
Long-hitting Belgian Colsaerts crushed American Bill Haas 5&4 and Sterne, also a power hitter, outgunned American Jason Dufner 1-up.
In the second round, Colsaerts will take on British world number six Justin Rose who won 2&1 against South Korean veteran K.J. Choi.
Sterne, who had lost in the opening round in his two previous appearances at the event, will next meet champion Hunter Mahan, who crushed Italy's Matteo Manassero 5&4.
Masters champion Bubba Watson beat Briton Chris Wood 2&1 and Ian Poulter, the 2010 champion, avoided a third consecutive exit at the first hurdle with a 2&1 victory over fellow Briton Stephen Gallacher.