McIlroy lost by six shots to Matt Kuchar after an amazing run of triple-bogey, double-bogey, double-bogey from the 15th, while Woods lost by one to Charl Schwartzel after a bogey on the 18th at the £3.2million Turkish Airlines-sponsored tournament .
The world's top two players are scheduled to face each other in the final match of Group One on Wednesday afternoon, but defeats for McIlroy to Schwartzel and Woods to Ryder Cup team-mate Kuchar in the morning would mean both players could not reach Thursday's semi-finals regardless of the result between them.
In regular match play McIlroy's seven at the 15th might not have been so costly, but with this week's format being medal match play - where the lowest 18-hole total wins one point - the 23-yeard-old admitted he "gave up a bit" after going three strokes behind with three to play.
"I was playing pretty well until the 15th, then hit a loose tee shot there and was messing about in the trees and making seven," said the world number one, who had not seen the course before today but at least arrived with plenty of time to warm up, unlike before his singles match at Medinah.
"Then I hit it into the hazard on 16 and was just trying to get the round done. I lost a bit of concentration, went a few behind and gave up a bit.
"If it was a different format and a different tournament it might not have got as out of control as it did, but that's just the way it is.
"But it's fine. I know what I need to do tomorrow. I need to go out and win both of my matches and see if that's good enough. In a way it could be a blessing that I'm not complacent and I go out and give it my best."
McIlroy had actually made two eagles on the front nine of the PGA Sultan course at Antalya Golf Club, holing from 15ft on the third and 50ft on the seventh, but his round unravelled after blocking his drive right into trees on the 15th.
He needed two attempts to get clear of the trees, but after coming up short of the green with his fourth shot, duffed his pitch and ended up holing from 10ft for a triple-bogey.
Woods, whose singles match at Medinah was also rendered inconsequential after Martin Kaymer ensured Europe would retain the trophy in the game ahead, was two under par after eight holes but ran up a triple-bogey seven on the ninth.
The 14-time major winner fought back with birdies on the 14th, 16th and 17th - the latter taking him level after Schwartzel bogeyed - only to bogey the last after failing to get up and down from a greenside bunker.
Asked about the prospect of facing McIlroy tomorrow afternoon, Woods said: "I have to take care of my match and we'll see in the afternoon. We have to both win in the morning.
"We're the two highest ranked players in the world right now and it will be a fun match either way, but it will obviously be a lot better if we both win in the morning."
In Group Two, Justin Rose beat Hunter Mahan by four shots and Lee Westwood beat Webb Simpson by one after the US Open champion bogeyed the 18th.
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Rose revealed he and Ryder Cup team-mate Ian Poulter had been inundated with congratulations for their triumph at Medinah while spending a few days in the Bahamas last week.
And the Englishman also offered his thoughts on Europe's next Ryder Cup captain, with Paul McGinley and Darren Clarke the current favourites.
"I think we have three or four good options," Rose said.
"I'm hearing Paul and Darren and maybe Paul Lawrie, but he is in the top 30 in the world and would probably want to play at Gleneagles.
"They (McGinley and Clarke) would both be great, I don't know if Darren might be more suited to America in 2016 as he is very popular over there.
"Paul will be very strategic and won't put a foot wrong tactically. He has holed the winning putt before and it means a lot to him. We have good options across the board."