The 35-year-old had six holes remaining and played them in two under par on Saturday morning to complete a superb 65 and finish 11 under par, two ahead of Day with England’s Justin Rose another shot back.

World number one Rory McIlroy began his round nine shots off the lead and saw his birdie putt on the first somehow hang on the edge of the hole without dropping, but the defending champion picked up shots on the second and fourth to move to four under.

McIlroy had leapt into contention by holing an eagle putt from 65 feet on the fifth, only to bogey the next after a poor approach into a greenside bunker and drop another shot on the eighth by tangling with two of the course’s 1,000 bunkers.

A par on the ninth took McIlroy to the turn in 34 and at four under par the 26-year-old was seven shots off the pace as the final groups made their way out on to the course.

“It’s amazing to be in the lead,” said Jones, who is making just his eighth appearance in a major.

“I’ve been in the lead in a tour event, but a major’s a different story. But I’m going to have fun with it and I’m pretty relaxed on the golf course.

“It’s hard to say if you ever feel a week like this coming. You’re a golfer, so you expect weeks like this. But I had some good weeks this year and I’ve had bad weeks and that’s the nature of the game.

“I’m a streaky player, I know that. I’m trying to get better at that part of my game. But I’m just managing my golf ball better this week than I probably have in previous years on tour and I’m putting well this week.”

Day has recorded nine top-10 finishes in his last 19 majors, memorably battling attacks of vertigo to finish ninth in the US Open in June and missing a birdie putt on the 72nd hole at St Andrews to get into a play-off for the Open Championship.

“I’ve put myself in the position, so the only thing I have to change is the end result,” Day said. “I just think that it’s easy for some people to get there quicker than others. Some people make it look easier than others.

“The experiences that I’ve had in the past in previous finishes, I think it’s setting me up for something big in the future. And I just really have to keep plodding along and really keep doing the stuff that I’m working on.”

The final pair were not due out until 1506 local time (9.06pm Irish Time), but the early starters were making the most of perfect conditions on the shores of Lake Michigan.

Phil Mickelson and Boo Weekley were both six under for their rounds after 13 holes to reach five under for the tournament, with France’s Victor Dubuisson six under with two to play and four under overall.

Weekley completed a 65 to set the early clubhouse target on six under par, with Mickelson five under after putting the finishing touches to a typically adventurous 66 containing nine birdies and three bogeys.

Mickelson, whose last victory was the 2013 Open at Muirfield, felt he could have threatened the lowest score in major championship history, which was equalled by Japan's Hiroshi Iwata with a 63 on Friday.

As well as his three bogeys, the five-time major winner three-putted the 16th from long range for par and said: “It could have been in the low 60s and possibly broken the major record. That would have been special. But you can’t make those kinds of mistakes.

“I finally, though, hit enough good shots. I hit a lot of good quality shots and made some good putts. I did the hard things very well and the easy things not so well today, but it’s a process of slowly getting it back.

“It’s been two years since I’ve been at my best and it’s a little disappointing that it’s taken so long. But I’m trying to be patient and rounds like these help because I see how close I am to finally being at my best.”