Play was suspended in the afternoon on Friday (local time), with 21 golfers on the course at TPC Southwind in Memphis as heavy rains flooded the area.
Second-round play in the opening tournament of the season- ending FedEx Cup playoffs will resume on Saturday morning before the third round begins off two tees in threesomes.
Fleetwood's 13-under 127 total was four strokes better than Americans Collin Morikawa and Akshay Bhatia.
Morikawa's five-under 65 on Friday included holing out from the fairway on the par-4 ninth for an eagle. Bhatia, the first-round leader after an eight-under 62, managed a 69 that included 15 pars.
England's Justin Rose also was tied for second at nine under with two holes remaining when the rains hit. Kurt Kitayama posted a seven-under 63 to finish at eight-under 132.
World No.1 Scottie Scheffler, who opened with a 67, had a roller-coaster round that included four bogeys and eight birdies, but finished at four-under 66 and stands at seven under.
The Aussie contingent was well off the pace, with Jason Day at one under after a second-round 68.
Cam Davis is also at one under, but is yet to finish his second round, currently even with the card after 10 holes.
Min Woo Lee, who opened with a 76, carded a two-over 72 to be eight over after two rounds.
A win by the 34-year-old Fleetwood would give the tour back-to-back first-time champions. Cameron Young won last weekend's Wyndham Championship, the final regular-season event.
"Maybe this weekend is the weekend," Fleetwood said. "We'll see."
In his 15th year as a pro, Fleetwood entered the second round one stroke behind Bhatia, but quickly overtook him by recording birdies in bunches. They came at Nos.2, 3 and 4 on the front side and at Nos.13, 14, 15 and 16 on the back nine.
The Englishman has won seven times on the European Tour, his last victory coming in the 2024 Dubai Invitational.
He has come close multiple times on the PGA Tour. Among his three top-10 finishes in 2025 is a tie for second at the Travelers Championship in June.
"Happy to put myself in with a chance over the weekend," Fleetwood said.
"I think that's exactly where you want to be and keep testing yourself. Yeah, it hasn't happened for me yet out on the PGA Tour, but I would much rather be up there and not quite get it done than not there at all."
Morikawa is trying to put his past two events - the Scottish Open and the Open Championship - behind him. He missed the cut in both, but is prospering after 36 holes in Memphis with a new caddie, Mark Urbanek, his fifth of the season.
The top 70 in the FedEx Cup points standings qualified for the St Jude.
Those who finish on Sunday ranked in the top 50 of the FedEx Cup points standings qualify for the BMW Championship, the second round of the playoffs to be held next week in Owings Mills, Maryland.
