McIlroy had lost both of his opening matches in Antalya - to Matt Kuchar and Charl Schwartzel - and needed to beat Woods and hope other scores and results went his way to have a chance of reaching this semi-finals.
But the world number one hit his opening drive into a water hazard to the right of the fairway and was forced to take a penalty drop, leading to a bogey five, while he then missed birdie chances at the second and third.
At one over par he was two shots behind Woods, who had narrowly missed birdie chances at the first and second before two-putting the par-five third for a birdie to move one under.
McIlroy was the only one of the eight players over par, with Group One leader Schwartzel three under after five holes and one ahead of Kuchar, while Group Two leader Justin Rose was four under after seven holes but only one ahead of US Open champion Webb Simpson.
McIlroy's already slim hopes were fading fast as the USPGA champion bogeyed the sixth to fall two over and five behind Woods, who had birdied the fifth and sixth.
Westwood meanwhile was continuing his brilliant round, reaching the turn in 28, seven under par, with five birdies and an eagle.
That left him four in front of Mahan and on course for a place in the semi-finals with a second win in three matches.