Joint overnight leader Ross Fisher (71) shares second with Thailand's Thongchai Jaidee and Francesco Molinari of Italy.
The 36-year-old sunk six birdies to fend off a six-man chasing pack which includes Englishmen Ross Fisher, Simon Wakefield and Simon Dyson.
Martin Kaymer, who carded a 68 at Kingsbarns, is the highest-placed Ryder Cup player, while England's Ross Fisher carded a 69, also at Kingsbarns.
Ian Poulter and Ross Fisher are tied with Tiger Woods and Steve Stricker, while Lee Westwood and Martin Kaymer lead Phil Mickelson and Dustin Johnson.
McDowell is two under and in a share of 30th - 10 behind Ian Poulter who is two ahead of Ross Fisher, Francesco Molinari and Thongchai Jaidee.
Harrington teamed up with world number number eight Luke Donald, Ian Poulter went out with Ross Fisher while Peter Hanson and Miguel Angel Jimenez completed the match-ups.
Ross Fisher was another to begin from the 10th at Carnoustie and recorded a double bogey at his opening hole, taking 41 to cover his first nine holes.
The European team also included Lee Westwood, Rory McIlroy, Martin Kaymer, Ian Poulter, Ross Fisher, Francesco Molinari, Edoardo Molinari, Peter Hanson, Luke Donald, Padraig Harrington and Miguel Angel Jimenez.
Ross Fisher, who started the day one shot behind Watson, suddenly found himself in a three-shot lead after birdies on the 1st and 2nd coincided with dropped shots from the American veteran.
The world number one led by three shots on Friday and his 71 was enough to move him to 13 under par, ahead of Tim Clark and Ross Fisher tied in second place.
Padraig Harrington and Ross Fisher will resume the successful partnership they forged in Wales over the weekend, while Westwood plays alongside Northern Ireland's Rory McIlroy and has tournament chairman Johann Rupert as his partner.
Ross Fisher was the most successful of the Ryder Cup players at seven under after carding a 68 at St Andrews, but was surprised by the severity of the conditions at the Old Course.
Paul Casey, still battling the rib injury which sidelined him for three months, Volvo World Match Play Championship winner Ross Fisher and Martin Kaymer, who is still struggling with a foot injury, sit on four-under.
The Twenty Ten course architects designed the final three holes almost specifically for this showpiece to test tired bodies and tired minds - but Ross Fisher's superb birdie on the par three 17th was matchplay at its best.
The fightback continued for Thomas Bjorn's side as Spanish pairing Miguel Angel Jimenez and Gonzalo Fernandez-Castano came back from two-down to defeat Ross Fisher and Nick Dougherty on the 17th to boost their hopes heading into the second day.
The 31-year-old Ryder Cup player, who led from the halfway point, recorded a 72-hole total of 271 (-17) to hold off the challenge of fellow-Englishman Ross Fisher -- whose best-of-the-week 64 was only one outside the West Course record.
At Turnberry, Watson and Ross Fisher, praying that his wife could delay the birth of their first child, were the threads of the last two days which lacked nothing in excitement and intrigue despite Woods having this time missed the cut.
For Europe, Graeme McDowell and Rory McIlroy played with Luke Donald and Martin Kaymer, Harrington and Peter Hanson went out with Lee Westwood and Ross Fisher with Edoardo Molinari and his brother Francesco taking on Ian Poulter and Miguel Angel Jimenez.
Englishman Ross Fisher shot a 69 and Scotland's Richie Ramsay a 71 as they joined Ernie Els in a tie for fourth place on eight under par, with Padraig Harrington two further back and England's Paul Casey moving up to five under with a 67.
BBC: Francesco Molinari & Lee Westwood vie for Shanghai lead
Poulter, joint leader overnight on nine under alongside Ross Fisher, moved three shots clear of the field after two early birdies but his first bogey of the week on the fifth, after a three-putt, and another dropped shot on 10 left him level at that stage with Fisher, Kaymer and Jaidee.
His solicitor, Ross Donnelly, told the court that Fisher was pleading not guilty.
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