Day was walking from the elevated tee on the par-three ninth - his final hole - on Friday when he suddenly fell to the ground, the 27-year-old needing several minutes of treatment before unsteadily getting to his feet and completing his round.
The world No 10, who underwent a range of tests after withdrawing from a PGA Tour event due to severe dizziness three weeks ago, was later diagnosed as suffering from Benign Positional Vertigo and visibly struggled during Saturday’s round.
However, after covering the front nine in 37 to fall seven shots off the pace, Day carded five birdies and one bogey to come home in 31 and set the clubhouse target of four under par which was matched by Masters champion Jordan Spieth, Dustin Johnson and South African Branden Grace.
Day, who finished second on his US Open in 2011, joint second in 2013 and fourth last year, said: “I didn’t feel that great coming out early, I felt pretty groggy on the front nine just from the drugs that I had in my system, then kind of flushed that out on the back nine.
“But then the vertigo came back a little bit on the 13th tee box, and then I felt nauseous all day. I started shaking on 16 tee box and then just tried to get it in, really.
“Last year I didn’t play the round after I had vertigo (at the Bridgestone Invitational) and this one was worse. I think the goal was just to go through today and see how it goes.”
Caddie Col Swatton said Day had almost retired three times but added: “He has played well in the US Open before and is playing well in this one. He just dug deeper than he ever dug before. It was really, really impressive.”
Day’s performance recalled memories of Ken Venturi’s victory in the 1964 US Open, the last year the final 36 holes were played in one day.
In oppressive heat, Venturi showed signs of dehydration after a third round of 66 and a doctor recommended he stop playing because it could be fatal. However, Venturi ignored the advice and shot a closing 70 to win his only major title.
“I was lying next to my locker and Dr Everett says, ‘I suggest that you don’t go out. It could be fatal,’” Venturi recalled in 2011 when the US Open returned to Congressional.
“I looked up at him and I said, ‘Well, it’s better than the way I’ve been living.’ I got off the floor and I do not remember walking to the first tee. I don’t remember the front nine until I started coming into it.”
Spieth is looking to become only the sixth man, after Craig Wood, Ben Hogan, Arnold Palmer, Jack Nicklaus and Tiger Woods, to win the Masters and US Open in the same year.
The world number two can also become the first player since Gene Sarazen in 1922 to win multiple majors aged 21 or younger, not to mention getting halfway to an unprecedented calendar grand slam.
“I will think about it a little bit because I want to win two in a row, but once I get out on the course tomorrow I will just be focused on the round and how to separate myself from the pack,” said Spieth, who set numerous records on his way to victory at Augusta National in April.
“I think as I sleep on it and wake up there will certainly be some nerves. It’s not like I’m a veteran at this by any means.
“But by the time we tee off, if I can convince myself that I’m free rolling, I’ve got one of these and the other guys are trying to chase their first.... I know how hard it is to chase your first and close it out.
“If we can use that winning formula we had back in April, mentally, then all it comes down to is can I just pull off the shots. It’s all on execution. I’m going to need to execute a little bit better, because mentally I think I’ll be strong enough to pull it off.
“I knew that even par was a really good score starting the day, but when I get to seven under for the tournament [after birdies on the second and third] I don’t want to finish at four under, no matter where you’re playing.
“I didn’t drive the ball extremely well and then when I had my opportunities, I had two eagle putts that I three-putted. So I had four three-putts today.”
Johnson took a three-shot lead into the final round at Pebble Beach in 2010 but collapsed to a closing 82, while a two-shot penalty for grounding his club in a bunker on the 72nd hole of the US PGA two months later cost him a place in the play-off.
“I’ve been in the situation a few times so I know how to handle myself. I know what it takes to get it done,” said Johnson, who held a two-shot lead after his fifth birdie of the day on the 12th, but then ran up a double bogey on the next.
“And tomorrow I just need to go out there and focus one shot at a time. And we’ll see what happens.”
Grace briefly held the lead after birdies on the fifth and eighth but dropped three shots in the next five holes before a birdie on the 15th.
“I actually played some great golf and the concentration slipped a little bit around the turn,” Grace said.
“I’m still happy. We all dream of this and we all practice for this, so it’s a matter of fact if you grab it or you don’t.
“I’m stoked. I can’t wait. To go into a tournament like the U.S. Open, having a chance to win my first major is something special.”
Harrogate’s John Parry shot a third round 71 to be 10 shots off the lead.