Adam Scott tamed Lytham again with a smooth 68 to lead the British Open by four shots from Graeme McDowell and Brandt Snedeker after a gripping third round in the sunshine on Saturday.
Australian Scott picked up three shots around the turn to surge clear of his playing partner and overnight leader Snedeker who imploded with six bogeys before a brave birdie on the last hole gave him a round of 73 and a seven-under total of 203.
McDowell delighted the packed galleries with three late birdies to complete a rock-solid 67, the 2010 US Open champion from Northern Irishman grinning broadly in the heat of battle as he stayed in the hunt for a second major title.
Woods, bidding for his 15th major, roared back after two early bogeys to card a level-par 70 and the former world number one finished in fourth spot on 204, one stroke ahead of three-times major champion Ernie Els and American Zach Johnson.
Scott started his round with six pars in a row and with his belly putter on fire, birdies at the seventh and eighth gave him real momentum.
The 32-year-old moved five shots clear of the field with another birdie on the 11th and after missing a short putt to bogey the 13th he calmly parred the last five, helped by a brilliant wedge to escape from a bunker by the 17th green.
Snedeker, sporting a bright pink shirt, made his first bogey of the tournament at the fifth hole and his second followed immediately when he found a Lytham bunker for the first time to drop back to eight under.
He clawed a shot back with a delicate chip to set up a birdie at the par-five seventh but Scott matched him to move ahead.
Snedeker suffered his third bogey at the eighth and the Australian sank a monster putt on the same green to sprint three clear.
Clearly rattled, Snedeker bogeyed the ninth as well after finding another bunker and Scott calmly made par to stretch his advantage to four.
The American dropped further shots on 11 and 14 but he rallied superbly with a birdie on the 16th and sank a 20-foot putt on the 18th to remain in contention for his first major title.
Woods recovered from bogeys at the first and third with a clutch of birdies at six, seven and nine to go to seven under.
A return to the metronomic golf which brought him two opening rounds of 67 led to five successive pars but a careless putt on the 15th green dropped him back to six under.
Els picked up two shots in the first seven holes to get to five under and after bogeying the 14th he made another birdie on 17 to stay in the hunt for a second Open title and fourth major.
World number one Luke Donald made an early birdie but took two shots to escape from a bunker next to the sixth green.
The ensuing double-bogey stalled his progress and the Englishman carded a 71 to finish well off the pace on one under. World number two Rory McIlroy continued to struggle on the Lytham links with a scrappy 73 to finish five over and third-ranked Lee Westwood's wait for a major title will continue after he went round in 71 to end on four over.
"I couldn't really muster up anything out there today," McIlroy told reporters.
"It wasn't difficult to get myself up for it but it is hard to keep yourself going when you know you are out of the tournament.
"There are definitely chances out there for a low score but it is tough. The scores aren't great out there today but you need to control your ball and keep it on the fairway."
Two former Open champions endured miserable rounds after just making the cut, five-times winner Tom Watson carding a 76 and John Daly 77 to finish at nine and 10-over-par respectively.
India's Anirban Lahiri caused the biggest cheer of the day with a hole-in-one, the first of the tournament, sending a nine-iron 150 yards into the cup.
"Just when I thought this experience was fantastic, it gets even better," said the 25-year-old after going round in 70 for a level-par total of 210. "It's just been fantastic."