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 countryman 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 said.
"I now need to win both my matches today to advance. I just struggled for a bit of motivation out there."
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 will now meets his Ryder Cup team-mate Woods this morning and Schwartzel in the afternoon.
Woods began his day 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.
He said: "It came right down to the wire but I can't believe how far that second shot flew into the back bunker.
"Despite the outcome I really enjoy the format."