Woods is still seeking his first PGA Tour win since that 2013 WGC-Bridgestone Invitational, but he came close with a thrilling No. 2 finish at the PGA Championship last month.
Needing a final-hole birdie to join Rose, Woods attacked the par-five green in two and posted a two-putt gain from 30 feet to get to seven under and ensure he will be out in the final group on Saturday.
Woods marched up the 72nd hole with rock concert scenes unfolding behind him as thousands of fans ignored security and police officers to walk the fairway and soak up the occasion.
"But I just think that what I've gone through and what I've dealt with, I've gotten lucky, to be honest with you".
Justin Rose plays his shot from the third tee during the third round of the Tour Championship golf tournament at East Lake Golf Club.
Nicklaus, who ended a two-year barren run by winning the 1980 US Open, was himself delighted to see Woods back at the pinnacle of the sport, tweeting: 'My congratulations to @TigerWoods on winning the @playofffinale!
"Certainly, this is going to be up there as one of my better accomplishments I've had [if I win]", Woods told NBC Sports before the tournament was over. "The fight and the grind and the tough conditions".
"As the year progressed I proved that I could play, I found a swing and put the pieces together and I knew I could do it again".
"It's simple math; if I (shoot even par) the guys behind me have to shoot 67 to force it into extra holes ... that helps".
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"I feel good about it".
"I was having a hard time not crying coming up the last hole", Woods said.
In the final round of the 2018 TOUR Championship, Justin Rose landed in the top five to jump up the rankings and win his first ever FedExCup.
The 14-time major champion and overnight leader closed with a one-over-par 71 and at 11 under he finished two shots ahead of runner-up Billy Horschel (66).
Woods now goes to France, where he'll play in the Ryder Cup with the rest of his US teammates.
Woods, who returned in January after missing nearly the entire previous two years with a debilitating back injury, held a three-shot advantage heading into the final round.
Rose collected £7.6m ($10m) as the FedEx Cup victor while Woods, who finished third overall, won an additional £2.29m ($3m) in prize money.
He cooled off on the back nine en route to a 12-under 198 total, while Englishman Rose recovered from a bogey, bogey start to card a 68.