Russell Henley and Kevin Kisner finished the week in 10 under and a share of third spot, with Casey in fifth place ahead of US Open champion Brooks Koepka.
Thomas started the day tied for fourth and made a late push with birdies on the 16th and 17th holes.
Simpson's approach may not work for every player, but after missing the Tour Championship the last two years it's clear he's looking to enjoy his return to the finale.
Both put on quite a show Sunday at East Lake. He got up and down from the green-side bunker on No. 9 to make the turn with a one-shot lead.
Open Champion Jordan Spieth (67) finished tied for seventh place alongside Spain's Jon Rahm (69) and Tony Finao (66) of the US.
Dustin Johnson, the No. 3 seed, has been sputtering along.
Sergio Garcia has four birdies on a bogey-free round so far.
"It's awesome just because I feel like I played so well this year", Thomas said, per James Corrigan of The Telegraph. I can't wait to get home, hopefully with a nice bonus from this week.
The reshuffle is conducted six times per year, and it ranks the players together in these three categories based on their season-to-date FedEx Cup points. He had to settle for a 70 and headed straight for the practice area. When it mattered most, Casey's putting touch deserted him; he made a four at the last to spare the ignominy of being the only player in the Sunday field not to post a birdie.
Xander Schauffele snuck this one in, but in the end, a win is a win.
"Since my first appearance in 1998, I have always loved playing in the Solheim Cup".
His birdie putt from exactly 12 inches looked a mere formality on TV but his nerves were on full display when he pulled the tap-in slightly and it did a near full circuit around the lip of the hole before dropping in.
Xander Schauffele. The PGA Tour rookie who won at the Greenbrier is making the most of his first trip to the Tour Championship, shooting 65 on Saturday.
The FedEx Cup victory no doubt clinches the PGA Tour's Player of the Year Award for Thomas. "I'd like to know how he dealt with that", said Thomas, referring to Spieth winning two Tour events but no majors in 2016.
Casey and Simpson are enduring long droughts.
Jason Day has squandered his last chance to ensure 2017 wasn't a winless year.
Casey has the best first round scoring average on the PGA Tour this year but a final round average of more than 76 strokes speaks for itself. The last time the Tour Championship victor did not claim the FedEx Cup title was in 2009 when Phil Mickelson won the tournament and Tiger Woods claimed the overall trophy.