Rai was at six under par through 16 holes when the opening round at Riviera Country Club was halted by darkness on a wet and windy Thursday in Los Angeles.
McIlroy revelled in the testing weather as he shot a five-under 66 to sit tied second with winless American Jacob Bridgeman (66), with New Zealand's Ryan Fox (67) a shot further back.
The rain that formed puddles on the already soft greens led to a three-hour stoppage. Players returned to far more difficult conditions with a wind that was strong and cold, and putting surfaces with a rare combination of being super soft and super quick.
Australians Adam Scott (70), Min Woo Lee (one under through 10) and Jason Day (one under through 14) were among nine golfers tied 20th.
Scott managed to counter his double bogey and two bogeys with five birdies while both Lee and Day held steady with pars and a single birdie each.
Meanwhile, Scheffler struggled in the opening round for a third consecutive week and was at five over par through 10 holes after racking up a double bogey and three bogeys to share last place in the 72-man field with Keegan Bradey (76).
McIlroy felt his mental approach proved a big help as he mounted his challenge.
"If you had asked me 10 years ago, I didn't enjoy these conditions, but it's been a shift in a mindset and maybe just a continuation of trying to build upon the skill set that I have," he said.
"Then when it does get to conditions like this, I'm a lot more prepared. I wouldn't say I enjoy them, but I can certainly handle them better."
Bridgeman, who reached the 2025 Tour Championship and is in the signature events for the first time, made his debut at Riviera with 15-foot eagle putt on the par-5 opening hole.
He was at his best when play resumed and the wind peaked, picking up five birdies in a 10-hole stretch and missing only one green after the delay.
"I think one of my strengths is flighting shots down, hitting shots where people don't really know how far it's playing, what the number actually is and just kind of feeling it out," Bridgeman said.
Collin Morikawa, a Los Angeles-area native who won last week at Pebble Beach, was in a seven-way tie for fifth place at three-under after posting a 68.
"Nice to get off to a good start and kind of be around the lead," Morikawa said. "This course is going to play very different, I think, the next three days, not quite with the softness and speed of the greens but just score-ability with the wind being down."
-with AAP, The AP
