Rai stormed to a maiden major title with an impressive three-shot victory at Aronimink Golf Club, where he carded an eagle and four birdies - including one from 70 feet - over his last 10 holes to pull clear of a congested leaderboard.
The Englishman closed a five-under 65 to finish comfortably ahead of two-time major winner Jon Rahm and overnight leader, after a Sunday where 30 players entered the final day within five strokes of the lead.
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Pre-tournament favourite Scheffler was among those starting Sunday five back as he looked to defend his title and register a fifth major title in as many years, only for him to finish tied-14th after mixing four birdies with three bogeys in a final-round 69.
The world No 1 squandered six chances from inside five feet over the week and finished 72nd of the 82 players who made the weekend in strokes-gained putting, with his performance on the greens preventing him from finishing further up the leaderboard.
"I'm pleased with how I battled," Scheffler told Sky Sports. "I battled really hard all week, I just couldn't get anything going on the greens. I feel like I gave myself a good amount of opportunities.
"Today was the day I hit a lot of greens, I just couldn't hole anything. That was the story of the week for me - it was just a matter of not holing putts.
"When I look back on a week like this, I feel I've had a really good year on the greens and to have a disappointing week on the greens at a major is a tough pill to swallow."
How three holes cost McIlroy another major title push
McIlroy was bidding to become the first player since Jordan Spieth in 2015 to win the first two majors in a calendar year, having successfully defended his title at The Masters last month, with the world No 2 starting the final round three strokes back.
The six-time major winner holed from 10 feet to save par at the first and got within two of the lead after birdieing the second, although only added one birdie and one bogey during the remainder of a final-round 69.
McIlroy failed to capitalise on a 379-yard drive into the par-five ninth and hit his tee shot into the rough at the driveable 13th, with a par at the 16th seeing him end the tournament even-par for the week on the par-five holes.
When asked what stopped from being closer to Rai's winning total, McIlroy: "I think not birdieing the two par-fives and making the bogey at the drivable par-four 13th.
"To me I felt like I played the golf I needed to play the rest of the way. If I birdied the two par-fives and turned that five into a three on 13, the day looks very different.
"Looking back on today's round, I would say those three holes [cost me]."
McIlroy's tied-seventh equals his best at the PGA Championship since winning the Wanamaker Trophy for a second time in 2014, with the Northern Irishman recovering from an opening-round 74 to post a 35th top-10 of his major career.
"I figured a few things out after Thursday and I played good golf for the last three rounds," McIlroy added. "I felt like I left a couple out there probably Friday and Saturday and then today, so maybe I didn't get the most out of my rounds.
"I played better and I gave myself a chance - that's all I could really ask for after the start. I'll rue three holes today that I didn't take advantage of and that's the difference between (tied-seventh) and having a realistic chance to win."
What's next?
The PGA Tour heads to Texas for The CJ Cup Byron Nelson at TPC Craig Ranch, where Scheffler returns as defending champion. Early coverage begins on Thursday from 12.45pm on Sky Sports+ and 5pm on Sky Sports Golf.
McIlroy is set to to take two weeks off before returning at the Memorial Tournament from June 4-7, while the next men's major is the US Open at Shinnecock Hills from June 18-21, with both also live on Sky Sports Golf. Get Sky Sports or stream with no contract.
