After toiling at Augusta National in April where he eventually ended in a tie for 45th, Rahm endured a start to forget and looked far from at ease with his own game.
Having spent the early part of the round in and out of the rough he rallied wonderfully but his frustrations were clearly evident when he tossed his iron into the fairway after pulling his approach to the 16th green.
However, birdies on the 17th and 18th, his fourth and fifth on the back nine, completed a superb damage limitation exercise for the Spaniard.
Scheffler is playing his first tournament since becoming a father. Like McIlroy he is also chasing a third successive victory after winning the Masters and RBC Heritage in April before taking some time off for the birth.
And he made a stunning return, holing out from the fairway on the first but that was the high point in a round that also showed elements of rustiness, with some uncharacteristic mis-hits into greens.
“I’d like to clean up a few of the mistakes,” he said before adding it was “overall a solid round”.
Cameron Smith, the 2022 Open champion, who remarkably saved par on the seventh hole after playing his second from the water in bare feet, finished among a group on three under, alongside Norway’s Viktor Hovland and England’s Aaron Rai.
Jordan Spieth, who is making his seventh attempt to become the sixth player to complete the Grand Slam of winning all four majors, started with a solid 69 to be level with his good friend and two-time winner Justin Thomas, who was well supported by his hometown crowd in Louisville, Kentucky.
Matt Fitzpatrick birdied the last to join Spieth and Thomas, while European Ryder Cup captain Luke Donald, who was in the first group out at 07:25 local time, carded a one-under 70. Fellow Englishmen Justin Rose and Matt Wallace also carded 70s.
Tyrrell Hatton is one further back while Tommy Fleetwood signed for a one-over 72.
Tiger Woods, who won the 2000 US PGA title at Valhalla to claim the third leg of what would become his ‘Tiger Slam’, conceded he “struggled from tee to green” after closing with successive bogeys as he also posted a 72.