Johnson, Hideki Matsuyama and Kevin Chappell all carded opening rounds of 66 at East Lake as McIlroy recovered from three-putting the first.
Johnson will secure the $10m (£7.7m) prize money on offer in the FedEx Cup if he wins in Atlanta, with a top-five finish likely to be enough.
McIlroy must win to have any chance.
Johnson - the US Open winner - birdied three of the first six holes and then the last after a 359-yard drive to move into a three-way tie for the lead.
McIlroy, who needs to win with Johnson finishing tied second or worse, bogeyed the first and then hit sixes at both the seventh and eighth holes during a rollercoaster round.
But seven birdies in total, including four in a row from 12 to 15, put him back into contention.
"It would be OK for the Ryder Cup next week I think, playing like this," McIlroy said on Sky Sports.
"I said to JP [Fitzgerald, his caddie] out there, I am mixing a lot of bad with a lot of good so if I can eradicate the mistakes, seven birdies around this golf course is pretty good and as you can see, once I get a couple of birdies I get some confidence and momentum."
Jordan Spieth, who won the FedEx Cup last year, also hit 68 to tie with McIlroy on two under par.
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FedEx Cup leader Dustin Johnson shared the overnight lead at the Tour Championship in Atlanta with Rory McIlroy two shots off the pace.