World number five Day, two ahead of Spieth overnight, never relinquished his lead as he closed with a five-under-par 67 on a blustery afternoon of hazy sunshine at Whistling Straits to post a major record low of 20-under 268.
The previous best at a major was the 19-under 269 by Tiger Woods when he triumphed by eight shots in the 2000 British Open at St. Andrews.
Day fended off the challenge of Spieth, who had been bidding for a rare third major victory in the same year, with four birdies in the first seven holes, followed by three more after the turn.
The 27-year-old Australian, who had previously recorded nine top-10 finishes in the majors -- six of them in the top four -- had to wipe tears from his eyes before he tapped in a one-foot putt for par on the 18th green.
Spieth, the Masters and U.S. Open champion, had to settle for second after closing with a 68 and securing the number one ranking for the first time, at the expense of Rory McIlroy.
Day, who was embraced by his pregnant wife Ellie as he made his way off the green, became the fifth Australian to win the PGA Championship after Steve Elkington (1995), Wayne Grady (1990), David Graham (1979) and Jim Ferrier (1947).
"It's an amazing feeling," a visibly emotional Day told CBS Sports after being presented with the coveted Wanamaker Trophy, which he hoisted high in celebration.
"Winning the PGA Championship is very special. I felt no one was going to stop me today. I played fantastic, through the whole round. Even though I made a couple of mistakes, I really felt good about my game.
"Just to be able to finish with a birdie on 16 and two pars on 17 and 18 felt fantastic. I never expected to be here. I can't say anything else because I'm going to cry."
South African Branden Grace, who pulled within a shot of Day's lead after making four birdies in five holes from the third, signed off with a 69 to place third at 15 under.
CONFIDENT START
Day made a confident start to the final round, although he stumbled just before the turn with a bogey at the eighth after driving into a bunker.
And he was in danger of dropping another shot at the ninth after chunking a wedge approach shot from the middle of the fairway.
He pitched his third shot to nine feet and sank the clutch putt to salvage par and go to the back nine with a spring in his step and a two-shot lead.
Day picked up further shots at the 11th and 14th to move four strokes clear and could afford the luxury of a bogey on 15 before finishing birdie-par-par.
Spieth, who ended his remarkable 2015 campaign in the majors with two wins, a tie for fourth and a runner-up spot, was lavish in his praise for Day's performance in the final round.
"He was sitting there swinging as hard as he could off the tee, and every single drive was right down the middle of the fairway," said the 22-year-old American.
"Jason ... it was his day. He played like a champion and he fully deserved this win."
McIlroy, back in action this week to defend his PGA Championship crown after being sidelined with an ankle injury, shot 69 to finish 17th at nine under.
(Editing by Andrew Both)
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