Rose was a 17-year-old amateur at Royal Birkdale in 1998 who holed out for par on the final hole to tie for fourth.
Rose trails Bryson DeChambeau, who won the first two playoff events, in the FedEx Cup standings.
Woods, coming back from injury, made the Tour Championship for the first time since 2013.
Rose got a lucky break in the playoff when his approach shot landed in a skybox but ricocheted back toward the hole and stopped just off the green. Delighted to be world No. 1.
"The belly putter was a tougher transition than I thought, and I kind of fell off the radar there for a little while".
Three-time major victor and former world number one Jordan Spieth carded a three-over 73 for his final round to finish tied-55th and subsequently drop from 27th in FedEx Cup points to 31st, meaning he will miss out on the Tour Championship for the first time since turning pro.
Speaking of his achievement, Rose told Sky Sports: "To get to world No 1 is unbelievable, and I can say now in my career I've been the best player in the world".
As usual, it crowded around Tiger Woods.
"When you talk about your career, those are the three highlights (winning a Major, playing in the Ryder Cup and being World No.1)".
"To have a chance to win again, this year, it's a very positive feeling", Woods said. "It made me feel calm, which is rare".
Spieth was keen to play down the severity of the situation after his disappointing final-round 73 in Philadelphia, but he hinted he was expecting to be hit by a fine rather than a ban. The top 30 players in the FedEx Cup standings will take part in that tournament. The top 30 on a season-long points list advance to next week's Tour Championship in Atlanta.
Players are required to play in 25 events in a season or risk a fine; Spieth played in 24 events and was clearly banking on making East Lake his 25th. Spieth is the first player to violate the policy, which began a year ago.
"I turned pro at 18 and it took me 20 odd years to get to world No 1, but my advice would be to just dedicate yourself to improving, to learning, to trying to get better".
Unlike most tournaments on the PGA Tour, there is a smaller field to split the $9 million prize pool with as the FedEx Cup playoffs have narrowed down the players eligible to compete over the past two weeks. Bradley shot a 64, Rose a 67, Schauffele a 67, Woods a 65, Horschel a 64, and McIlroy a 68.