The 42-year-old from Dungannon overcame rain, wind and all the inevitable pressures of setting the pace in the biggest event in golf to fire a superb third-round 69 on Saturday.
But it came as his Northern Ireland compatriot Rory McIlory's hopes of adding The Open championship to his US Open victory faded, with a four over finish of 74.
American Dustin Johnson - who was one of two players to shoot a round of 68 - is now the chief danger to Clarke's bid to continue the remarkable story of Irish success in the last four years.
After Dubliner Padraig Harrington's back-to-back Opens and a US PGA title as well, Graeme McDowell captured the US Open last year before McIlroy succeeded him last month.
Now their fellow Northern Irishman Clarke, playing the 54th major of his career but without a top 10-finish in them for a decade, stands five under par and looks down on the rest of the field.
He knows he might never have a better chance to lift the Claret Jug denied him in 1997 by a closing 65 from American Justin Leonard.
But Johnson has a burning desire too after what happened to him last season.
The 27-year-old led the US Open by three with a round to go at Pebble Beach, but let in McDowell by crashing to an 82.
Then two months later he thought he was in a play-off for the US PGA after a closing bogey, but was given a two-stroke penalty for grounding his club on sand on the final hole.
In joint third place on two under are Thomas Bjorn, the Dane who blew the 2003 Open at the course after leading by three with four to play, and American Rickie Fowler.
Glover shot 73 playing with Clarke, while Fowler matched Johnson's 68 partnering fellow 22-year-old Rory McIlroy, whose chances of a US Open-Open double hang by a thread now with a 74 dropping him nine behind.
That included driving out of bounds on the long 14th and running up a double-bogey seven, but McIlroy did then recall that in 1999 Paul Lawrie was 10 back at Carnoustie and won.
"Ten's been done before," McIlroy said. "You just have to keep hope.
"To be two over after 13 was a pretty decent effort. You've done so well to keep yourself in it and with half of Kent on your left to hit it right was a bit disappointing.
"That was a tough one to take. It's big setback. I obviously wanted to get closer to the lead rather than further away."
Last year at St Andrews McIlroy led by two after a major record-equalling opening round of 63, but followed it with an 80 in gale-force winds.
He did well to fight back to third place there, but added: "It seems this tournament more than anywhere else you need to get a good draw and it has not really worked out for me this week.
On the drive at the 14th he stated: "The moment I hit it I thought it was out of bounds, but then it started to hang on and I thought it could be okay.
"I think it bounced in bounds and then went out."
He was forced to hit another off the tee and missed the green with his fifth shot.
Strong winds and heavy rain had made life extremely tough for the early starters, with 61-year-old Tom Watson using all his experience to set the early target after a brilliant 72.
Watson, who carded the 15th hole-in-one of his career in the second round on Friday, opened with six straight pars before taking advantage of the downwind par-five seventh, finding the green in two and two-putting for birdie.
Fellow American Gary Woodland had been the only other player to break par on the front nine at that point, the 27-year-old out in a remarkable 33 after birdies at the fifth and seventh, before coming home in 41.
Three bogeys in five holes on the back nine halted Watson's progress, but the five-time Open champion holed from 20ft for birdie on the 16th before three-putting for bogey on the 18th from just short of the green.
It took almost two hours before his four-over-par total was beaten by France's Raphael Jacquelin, but with the weather easing a repeat of 2009 - when he had a putt to win on the 72nd hole before losing in a play-off - was looking highly unlikely.