Torrential rain began lashing Antalya Golf Club shortly after the morning matches in the eight-player event were completed, forcing organizers to postpone the four afternoon matches to Thursday with the semifinals staged afterward.
On Wednesday, Schwartzel birdied three of his last four holes to shoot a 1-under 70 to McIlroy's 71.
"You can't really do much about that," said McIlroy, adding: "I played a bit better than yesterday."
Woods recorded his first victory at the exhibition tournament with a 67 to defeat Kuchar by five strokes. Woods fell to Schwartzel by one shot on Tuesday.
The top-ranked McIlroy has only an outside chance of advancing in the $5.2 million event after losing by six shots to Kuchar on Tuesday and by one stroke to Schwartzel in the medal match-play format.
"In my match now against Tiger, I will be out to get back a bit of pride and at least leave here winning one match," McIlroy said. "I now don't have much to play for, so I would like to beat him so he doesn't go through to the semifinals and also to get some bragging rights.
"There is always an added edge when you play against a player like Tiger, and there were a few chances this year when we could have gone head-to-head in the bigger tournaments but it didn't quite happen. So I am still looking forward to next season when we can go head-to-head down the stretch -- and bragging rights from this week will help a little bit."
Victory for McIlroy over Woods would bring him $450,000 in prize money. Even a loss to the 14-time major winner will carry a $300,000 check.
In other morning matches, Rose defeated Westwood with a round of 66 to his European Ryder Cup teammate's 69. Simpson, the U.S. Open champion, had a 65 to Mahan's 67 for his first victory, leaving his fellow American winless.
The event is sponsored by Turkish Airlines, with the winner earning $1.5 million.