Spaun held a share of the lead overnight but seized it outright thanks to a couple of late clutch putts in his second round.
The 31-year-old American sank a 13-foot birdie putt on his penultimate hole before holing another seven-footer on the last to finish on 11-under 129 at TPC Southwind in Memphis, Tennessee.
"I feel good. It's exciting," Spaun said. "Still a lot of golf left. Just going to try to keep doing what I've been doing the last two days and hopefully it will pay off.
"I worked on some good things in the past couple weeks that are starting to pay off. Got a nice feel with my swing and just trusting it. And the putter is working, too."
Austrian Sepp Straka, who had missed six cuts heading into this event, lies in second place a shot behind alongside American Troy Merritt, with American Denny McCarthy another stroke adrift.
British Open champion Cameron Smith of Australia shared fifth on 132, just three shots back, after making his move with a 65. He is tied with Americans Brian Harman, Ryan Palmer and Tony Finau.
The tournament is the opener of the FedEx Cup play-offs, a series of three events wrapping up the PGA Tour season with a first prize of $18 million on offer.
This week's field features 125 players, but only the top 70 in the FedEx Cup standings will advance to next week's BMW Championship in Delaware.
Only 30 players will qualify for the Tour Championship at Eastlake in Atlanta, Georgia the following week.
Two-time FedEx Cup champion Rory McIlroy missed the cut after rounds of 70 and 69 left him one shot over the cut line.
World No 1 Scottie Scheffler also won't be around for the weekend after finishing on the same total.