In much more windy conditions overnight leader McIlroy bogeyed the first three holes and went from one ahead to three behind.
The 21 year old Northern Ireland's six at the long third saw him go left in two, he left his first chip short of the green, went to the far fringe with his next and then missed from ten feet.
Garcia had dropped his first shot of the tournament on the first green, but came back with birdies at the third and fifth to move 11 under par and two ahead of South African Thomas Aiken.
The Spaniard is seeking his first win since November 2008 and in that time dropped from second in the world to his current 79th and took time out to try to discover his zest for the game.
Woods, of course, last tasted victory almost 15 months ago, but after moving into contention with a superb second round 66 - the best of the day - he matched McIlroy by kicking off again with back-to-back bogeys.
At least he responded with a four on the 568 yard downwind third, but at six under after seven holes he had slipped from fifth to ninth and had five shots to make up on Garcia.
McIlroy let his fourth shot go on the short seventh, the hole where Raphaël Jacquelin had had the second ace of the tournament earlier in the day, but Woods fared even worse at the end of the outward half.
After failing to get up and down from a bunker at the eighth his approach to the next found the lake. With a double-bogey six he was out in a four over 39 and had dropped to 29th on three under - eight adrift of Garcia.
Scotland's Stephen Gallacher had moved into third spot at eight under, one behind Aiken and three behind Garcia, while McIlroy was in a tie for fourth.
As for World Number One Lee Westwood, he remained five under after 11 and was 13th, while Number Two Martin Kaymer was all the way back in 51st place, four over for the day like Woods and level par overall.
It left the German with little chance of the top-two finish he needed to dethrone Westwood.
Woods revived his flagging spirits with a chip-in eagle at the tenth and then an 18 foot birdie putt on the next to be six under and joint 11th with Westwood, while McIlroy finished the front on a high note too.
Despite driving into the rough on the ninth he hit his approach to 20 feet and made it for birdie to climb back into a tie for second with Aiken, who bogeyed it.
They were three behind Garcia, though, as he reeled off four pars in a row to turn in 34 - four better than McIlroy and five better than Woods.
Garcia bogeyed the 169 yard, par three 11th to allow McIlroy and Aiken within two shots of the lead, but the Northern Irishman stumbled to a bogey on the same hole to immediately give the Spaniard a shot back and slip back into a seven-strong pack tied for third.
That became fourth as Aiken parred the hole and was joined in second place by Denmark's Anders Hansen, who birdied the tenth.
Kaymer shot a four over par 76 to leave him tied for 48th, level par for the tournament, and with virtually no chance of deposing Westwood as World Number One this week.
A further bogey from Garcia at the 12th gave additional hope to the chasing pack.