In a dramatic finish, Day gave himself a great chance of retaining his title with an eagle at the last hole but Walker held his nerve to two-putt for par and the coveted Wanamaker Trophy.
"Sometimes things don't come easy and golf isn't an easy game," Walker said following Sunday's win in Springfield, New Jersey. "Day is a great champion and I wouldn't expect anything else -- eagle at the last.
Despite appearing calm and collected throughout a nerve-shredding back nine, Walker admitted he felt the tension out on the course.
"There's a lot of emotion going on out there, I'm not gonna lie. It's tough, it's amazing."
On the penultimate hole, Day missed a good chance for birdie to close the gap on Walker to one shot, something he would go on to rue.
The world No. 1 then opted for an iron off the 18th tee and followed it up with an exquisite approach shot that gave him the chance to finish his round with an eagle.
On his walk to the final green, Day threw his club in frustration as he heard the roar from behind him, signaling another Walker birdie at the 17th.
Walker's birdie putt looked to be missing right, but the stars aligned for the part-time astrophotographer
-- and the hole gathered the ball in.
It appeared as though the 37-year-old slightly over-hit his first putt on the 18th green, leaving himself with a tough three-footer to secure the title.
But in truth, the par was never in doubt as Walker completed a bogey-free final round of 67.
"It feels sweet, it's amazing," Walker told Sky Sports after his triumph. "I felt like something clicked last week and I brought it in this week."
He had played 187 tournaments before winning his first PGA Tour title in 2014, when he also had three top-10 finishes in majors.
Walker won twice last year to take his title tally to five, but the Oklahoma native hadn't been tipped as a contender at Baltusrol after missing the cut at the U.S. Open, Players Championship and British Open.
His victory means that, for the first time in five years, all four of the year's majors have gone to first-time winners.
Walker didn't hit a golf ball Saturday after bad weather forced play to be abandoned
, instead returning Sunday morning to shoot 68 and take a one-shot lead over Day into the final round.
"It's surreal, it really is," Walker said of his maiden major win. "I'm having a hard time putting words to it now."