At five under par overnight, McIlroy and MacIntyre had the opportunity to push on as the rain eased.
Only the Scot looked likely to take it.
Playing the opposite side of the course to the more celebrated names, he quietly picked up four shots in 10 holes to get to nine under par but after hitting a shot from a hospitality verandah as he scrambled a par on the long seventh, he bogeyed the final two holes as he raced to beat the fading light.
Meanwhile, McIlroy birded the opening hole but was unable to find his form on the greens before the double bogey at 12 wrecked his card. It now seems unlikely his long wait for a major victory will end here at the place where he won his last one in 2014.
Playing partner Justin Rose managed an eagle at the last to join him on five under par while fellow Englishmen Matt Wallace (67) and Aaron Rai (68) improved to seven and six under respectively.
Thirty-one of the past 34 winners of this tournament have been in the top 10 at the halfway stage.
Bryson DeChambeau, the 2020 US Open champion, is in that bracket after he shot seven birdies on his way to a 65 as he finished in near darkness to join Scheffler on nine under.
He was joined in the top 10 by 2023 runner-up Viktor Hovland who moved smoothly to eight under with a 66.
Lurking one place outside the top 10, 2023 winner Brooks Koepka matched magical iron play with inconsistent putting in his three-under 68. Five off the lead, the three-time champion remains a threat in this tournament.
