Rai became the first English winner of the Wanamaker Trophy in more than a century and the first non-American champion in 10 years.
The 31-year-old carded a brilliant five-under-par 65 to finish nine under overall, ending three shots clear of Spain's Jon Rahm and overnight leader Alex Smalley.
Rai surged clear with birdies on the 11th, 13th and 16th before effectively sealing victory with a stunning 69-foot putt on the 17th green - the second longest made all week.
"It is very surreal," said Rai, who has been dealing with an intermittent neck injury this season.
"It has been a frustrating season, so being stood here is outside of my wildest imagination."
American Justin Thomas briefly held the clubhouse lead after a 65 lifted him to five under, alongside Sweden's Ludvig Aberg and Germany's Matthias Schmid.
But Rai's accuracy off the tee and calm approach on Aronimink's punishing layout proved decisive as he steadily separated himself from the chasing pack.
"I definitely wasn't trying to hole that putt," Rai said.
"The shadow of the pin gave a really nice line for the last 10 feet so that helped with the visual.
"It just tracked really well - it was amazing to see it go in."
Rai becomes only the eighth Englishman to win a major since World War Two and follows Rory McIlroy, who defended his Masters title in April, in giving UK golfers victories in the first two majors of the year.
McIlroy closed with a one-under 69 to finish five shots behind after failing to capitalise on the par fives and bogeying the driveable 13th.
"I'm proud that I gave myself a chance," the world number two told BBC Sport NI.
"But there are three holes I'll rue - not birdieing the two par fives and then making bogey at the driveable par-four. Those three holes cost me a chance to win."
Rahm briefly shared the lead after birdies at the opening two holes but could not keep pace with Rai, while Åberg's challenge faded after three bogeys in four holes around the turn.
Defending champion Scottie Scheffler also failed to mount a charge, finishing seven shots adrift in a tie for 14th after another difficult week on the greens.
The world's top two players, Rory McIlroy and Scottie Scheffler, were left to reflect on what might have been after both fell short in the closing stages of the PGA Championship on Sunday.
Rory McIlroy's four under 66 in the third round of the PGA Championship gave him a fighting chance to claim another major.
Alex Smalley is in pole position for his maiden PGA Tour win at the PGA Championship, as her leads the field by two shots.
Rory McIlroy believes he remains firmly in contention for a second successive major title after producing an impressive second-round recovery at the PGA Championship on Friday.
