Day rolled in an eagle, four birdies and a par between holes nine and 14 at Whistling Straits late Saturday to shoot to the top of the leaderboard at 16-under-par.
But an ugly double bogey on 15 brought about by a woeful bunker shot spoiled much of the Australian's good work in his quest for a first major title.
Day recovered to birdie 17 and finish the day on 15-under-par. But he will be looking over his shoulder at a strong field closing in behind.
Jordan Spieth lies two shots back in second on 13-under-par as he looks to add to the Masters and U.S. Open crowns he has already claimed this year.
The 22-year-old is attempting to become only the third man, after Tiger Woods and Ben Hogan, to win three majors in a calendar year.
A remarkable six birdies and three pars on the back nine ensures he is adequately placed to do so.
England's Justin Rose looked all set to join Spieth on 13-under but dropped a shot at the last to finish the day 12-under-par alongside Branden Grace of South Africa.
Martin Kaymer, who won the U.S. Open the last time it was played at Whistling Straits in 2010, also retains a decent outside chance at 11-under par. As does Jones who faded badly on the back nine.
Jones had never led a major tournament before this weekend or finished higher than a tie for 30th position at one of golf's big shows.
The 34-year-old seemed to lose focus on on the back nine with bogeys on 15, 16 and a double bogey on 17 to finish at 10-under-par -- one ahead of Friday's leader Dustin Johnson.
Jones' late fade was perhaps brought about by extra golf he played earlier in the day.
Early Aussie rise
Both Jones and Day were forced to get up early and finish their second round Saturday morning after a thunderstorm curtailed play Friday.
It was Jones who initially looked more comfortable with the early start, moving a handy two shots clear by the time he was back in the clubhouse.
Jones added another birdie on the first hole as he teed-off round three a few hours later. He then moved three shots clear when Day acquainted himself with the Whistling Straits sand traps at the second.
But with just one more birdie on the front nine, the chasing pack was soon looming large in Jones' rear-view mirror.
When he was forced to play from the carpet of a hospitality suite after a wayward tee-shot on nine, clearing tables, bar stools and spectators out of the way to take his second stroke, it looked as if his lack of experience at the sharp end of major tournaments was beginning to tell.
Naturally, Day was only too eager to take advantage of his fellow Aussies difficulties. A birdie on nine was repeated with another on 10. An eagle on 11 took him into the outright lead. Two more birdies on 13 and 14 followed.
'Overall I'm very pleased with the way I came back on the back side,' Day later told sky Sports. 'The putter was rolling today which was great.'
'I feel good about everything. I played great all three rounds and I've just got to keep pushing. I'm going to go and work the irons tonight but I feel really confident in my ability to stay patient with myself.'
Keeping cool with the in-form Spieth breathing down your neck is easier said than done, however.
The World No. 2 sounded ominously confident when reflecting with the same broadcaster on his masterful back nine performance and chances come Sunday.
'Tomorrow looks like it will be tougher conditions,' Spieth said. 'We'll see what they bring, it's just about trying to limit the mistakes.
'If I can have a bogey-free round again I think I'll make enough putts to get it done.'
Rory rolls dice
Elsewhere on the course Saturday, defending champion Rory McIlroy started strongly with three birdies in the first five holes.
But the Northern Irishman, who missed last month's Open Championship in Saint Andrews after damaging ankle ligaments playing football with friends, faltered with bogeys on 6 and 8.
The back nine brought three more birdies but also a pair of bogeys to leave the World No. 1 nine shots off the pace at six-under-par.
The ever-popular Phil Mickelson was another to charge up the field early on, notching up nine birdies alongside three bogeys for a round of 65 to finish the day five-under-par.
It's been a lean couple of years for the 45-year-old lefty who last won a major in 2013. But he later told reporters he hasn't given up on claiming another grand slam title.
'I haven't been at my best for some time and I'm slowly coming back, he said. 'Each round I seem to hit more good shots and if I'm patient enough it will come back.'
Mickelson's 65 was matched by U.S. compatriot Boo Weekley who moved into a group, which also included McIlroy, Charl Schwartzel and Japan's Hiroshi Iwata, at six-under-par.
Iwata became only the 27th man to card a score of 63 at a major Friday but could only register a more modest 70 on Saturday.
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