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South Korean KJ Choi, trying to become the first Asian to win a major title, needed only to par the first three holes to stretch his lead from one to three.
That was because playing partner Greg Norman, the 53-year-old twice champion who had turned back the clock with two opening rounds of 70, bogeyed the first and third.
Harrington, in danger of withdrawing with a wrist injury before the start of the championship, resumed in a share of fourth spot as he continued to chase the dream of being the first European to retain the Claret Jug since James Braid in 1906.
He failed to get up and down from a bunker on the 421-yard second, but after going in deep rough two holes later he produced a heaven-sent chip-in for a birdie three to return to two over and then added another birdie from six feet on the short seventh to cut Choi's advantage back to two.
Norman was in third place, while one stroke further back on three over were American Jim Furyk and Open debutant Camilo Villegas, the Colombian who had finished his best-of-the-week 65 on Friday with a magical five successive birdies.
Northern Ireland's Graeme McDowell was in a share of sixth on four over, coming back from an opening three-putt double bogey six and bogey on the third with a birdie at the 346-yard fifth.
England's Ian Poulter was making a determined bid to stay well in touch as well. After seven holes he stood five over.
Fierce though the wind had been on Thursday the forecast even then was that Saturday afternoon would be worse and so it proved.
The tees at the sixth, 11th and 16th had been moved forward 13, 78 and 68 yards respectively as a result, but that was not enough to prevent some real horror stories.
American Sean O'Hair finished nine-seven, losing a ball at each hole, for an 80, while Lee Westwood four-putted the first green in his 78 and both Phil Mickelson and Ernie Els, seven over and nine over at halfway, almost certainly are out of it on 13 over after rounds of 74 and 76.
Yet through it all Mickelson's partner Ben Curtis, the American who was playing his very first major and was ranked 396th in the world when he won at Sandwich in 2003, posted a level par 70.
Having started the day in 38th place he then had a four-hour wait to see where a seven over aggregate left him with a round to go. In with a chance was the bottom line.
Highlight for the 31-year-old was a 165-yard nine-iron to the third which he initially did not like, but ended up loving because it went in for an eagle two.
In stark contrast to that Justin Rose, back on the links where as a 17-year-old amateur he finished a spectacular fourth 10 years ago, came to grief with an outward 42 containing a double bogey on the fifth and six bogeys.
Two more dropped shots quickly followed to leave him 16 over, while 2001 champion David Duval, joint fourth at halfway despite making only one cut all year and being 1,087th in the world, quickly slumped to eight over.
Duval started with a triple bogey seven, taking a penalty drop from the rough short right of the green, and then bogeyed the next three.
Jean Van de Velde was another struggling. Resuming four over, that soon became 10 over with a double bogey on the short fourth and two bogeys either side.
The duel to be top amateur between English pair Chris Wood and Tom Sherreard looks set to go to the wire tomorrow. With eight to play today Wood, from Bristol was nine over and with three to go his rival was 11 over.
Harrington three-putted the eighth for bogey, but still moved only one behind as Choi, having missed a five-foot chance on the fifth, was bunkered at the next and could do no better than a double bogey six.
With Norman taking five on the same hole it was Choi one over, Harrington two over, Norman three over and both Furyk and Villegas four over. Curtis, safely in the clubhouse, was up to 12th.
Harrington became co-leader when Choi let another shot go on the 457-yard eighth - and it was a four-way tie as Norman birdied the eighth and Furyk, fourth on the course in 1998, had birdied the eighth and ninth to match the Irishman's outward 34. They were all two over.
Rose completed a miserable 82, the highest score of his Open career, and had only two players beneath him at 18 over.
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