Right when he thought the tournament was in hand, Chappell birdied three of his last four holes.
Annes, where the Australian bogeyed his last four holes and finished one shot behind in the British Open.
Although Howell caught him with his third birdie in four holes at the 14th, he followed with back-to-back bogeys.
He birdied the final four holes, the first time that had ever been done on the way to victory.
Harrington had played 14 holes before the storm, and the three dropped shots came in the closing four holes.
Scott Stallings was 7 over through four holes and thrilled with the decision.
Molinari, one of Westwood's victorious Ryder Cup team-mates, began in ideal fashion with two birdies in his first four holes.
His drive usually doesn't travel more than 250 yards, making several of the course's long par-four holes too difficult for him.
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He birdied the next four holes in a row to right himself.
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Meanwhile, Howell was in fourth place on six-under overall after four holes.
Sergio Garcia responded to his last-round slump at the Open with an impressive 69, which included three birdies in the last four holes.
Defending champion Frederick Jacobson was also out of sorts as he dropped three shots in his first four holes, including a double bogey.
Mickelson is also eight behind the leaders after four holes of his second round, shooting pars after dropping a shot on the first.
After a late-night flight from Paris, Van de Velde bogeyed the first four holes at Glasgow Gailes and finished with a five-over 76.
Two years ago, Scott and Jason Day finished tied for second as Charl Schwartzel produced an astonishing final four holes to win the tournament.
Karlsson was four shots clear after seven holes after recovering from a bogey at the first with three birdies in his next four holes.
The 73-year-old South African, one of only five men to win all four major tournaments, made bogey at each of his last four holes.
Both finished with closing birdies on the par-five 18th to reach 12 under, Woods finishing strongly with three birdies on the final four holes.
Even on long par-four holes like No. 5, playing at 501 today, and No. 6, playing at 485 yards, he hit irons off the tee.
The decision was great news for Scott Stallings, who made a quadruple-bogey 8 on the third hole and already was 7-over par after four holes.
But he ran off three birdies on the next four holes, and made clutch par saves on the 16th and 18th to stay in the game.
He started fast with three birdies in the first four holes, He dropped a shot at the 15th but carded six more birdies for a superb round.
Three birdies and an eagle in the last four holes put defending champion Luke Donald back two off the lead, tied with Dane Anders Hansen in third.
McIlroy had vowed to improve on his opening round and hit three straight pars, but three bogeys in the next four holes left him floundering on six-over.
Despite finding water on the third, the 33-year-old pitched to three feet to save par and birdied three of the next four holes to move into pole position.
It was only last summer when Scott threw away the British Open by making bogey on his last four holes to lose by one shot to Ernie Els.
McIlroy found himself three down after four holes to his former management agency stablemate Westwood, but he staged a sterling recovery to win four of the next five.
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Donald's score of five-under-par for the last four holes also made sure he will be challenging Garcia, who admitted even he was shocked by how erratically he had played.
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