Northern Irishman McIlroy was beaten by American Matt Kuchar in the invitational eight-man matchplay event in Turkey while Group One rival Woods lost to 2011 US Masters champion Charl Schwartzel of South Africa.
In Group Two, English pair Lee Westwood (72) and Justin Rose (71) recorded respective victories over US Open champion Webb Simpson (73) and fellow American Hunter Mahan (75).
The two top in each section go through to the semi-finals of the $5.3 million tournament.
McIlroy had a nightmare late spell at the Antalya Golf Club, playing the last four holes in seven-over-par to finish with a 76 against Kuchar's one-under 70.
"I hit my drive into the trees on 15 and lost a bit of confidence," the US PGA champion told reporters.
"I now need to win both my matches tomorrow to advance. I just struggled for a bit of motivation out there today."
It was the first competitive round of golf for McIlroy and Kuchar since the Ryder Cup ended nine days ago.
McIlroy, 23, accompanied by tennis-playing girlfriend Caroline Wozniacki, was two shots behind at the turn in the strokeplay format.
Kuchar, wearing shorts and looking refreshed after a week's family holiday in Greece, said: "It was quite a match. I played really well on the front nine and was three ahead through 10 holes.
"I just thought I had to play mistake-free and hopefully Rory wouldn't get too hot," added the American.
"Then we were all square with four to go, he hits it right and makes a triple bogey and I go three up with three to go and I think both of us lost a little interest at that point."
Kuchar now meets Ryder Cup team mate Woods on Wednesday morning and Schwartzel in the afternoon.
Woods began his bid for the $1.5 million first prize with a birdie at the first but was then held up by a triple-bogey after finding water off the tee and three-putting.
He was level with Schwartzel on the 18th tee but the 14-times major winner found a greenside bunker with his approach and a bogey meant he carded a 70 to Schwartzel's 69.
"It came right down to the wire but I can't believe how far that second shot flew into the back bunker," said Woods.
"It means I now have to play 'Kooch' and try and win that match before facing Rory in the afternoon. Despite the outcome I really enjoy the format.
"It's not something we play very often. I had a three-shot swing go against me on nine and a two-shot swing in my favour at 17 when I birdied the hole and Charl bogeyed."
Westwood broke into a big smile when he chipped in from off the green at the 17th to take charge of his match with Simpson.
"I played a great shot there even though I did not have too good a lie," said the world number four.
"The ball was sitting down where TV cables had been but it just came out perfect. It landed in the right spot and as soon as it got on the green it looked like going in."