Wielding a red-hot putter, Irishman Harrington covered his final nine holes in a blistering six-under-par 29 to card a seven-under 64 in the first of the US PGA Tour's four lucrative FedExCup play-off events.
In pursuit of his first victory on the US circuit since the 2008 US PGA Championship, three-times Major winner Harrington piled up eight birdies and a lone bogey to finish a stroke in front of Americans Nick Watney and Brian Harman.
Spaniard Sergio Garcia, who ended a four-year title drought on the US PGA Tour by winning the rain-delayed Wyndham Championship on Monday, was among a group of four on 66 while FedExCup points leader Woods opened with a 68 and McIlroy a 69.
Harrington, who also has one eye this week on earning a late call-up for the European Ryder Cup team, was delighted with his putting on the challenging, 7,468-yard Bethpage Black layout.
"I've been playing well for quite a while, but this is the best I've putted, the best I've struck my putts, the best I've rolled the ball for a long period of time," the 40-year-old Irishman said after taking only 26 putts.
"We had super conditions today. Bethpage is a big, strong golf course, and we got it on a very calm day, which was in our favour."
Harrington conceded he had learned a valuable lesson about the scoring possibilities at a venue which has staged two US Opens from his American playing partner Troy Matteson, who eagled the fourth hole.
"Wow, an eagle! Imagine making an eagle at a US Open," smiled Harrington. "If anything, it really helped me because I could see that, 'Hey, this wasn't a US Open, there were birdies to be made.'
"So you have to get out of that mindset because level par isn't winning the tournament this week. It isn't a US Open," added the Irishman, who won The Barclays at Westchester in 2005 and tied for second at Liberty National in 2009.
Harrington hopes his sizzling form at Bethpage will help him earn one of two wildcard picks by European Ryder Cup captain Jose Maria Olazabal on Monday, though he accepts he is on the outside looking in.
"I'm sure if I went and had a look at the odds, I would be a long-shot to make the team," the Irishman said.
Olazabal later said at the European Tour's Johnnie Walker Championship in Scotland that Harrington would have to "at least win" at Bethpage to get picked.
Woods, the only triple winner on the 2012 US PGA Tour, expressed mixed views about his round after failing to make the most of soft, receptive conditions on a benign morning.
"I didn't quite hit the ball as well as I would like," said the 14-times Major winner who was followed by huge crowds as he launched his title bid in the company of world number one McIlroy and 2007 Masters champion Zach Johnson.
"I'm going to do some work this afternoon and work on a couple things that I know I need to shore up for tomorrow. But I'm very pleased with the way I putted. I putted great today."
Woods, who totaled 28 putts, ended the round level with fellow Americans Johnson and four-times major winner Phil Mickelson, Open champion Ernie Els of South Africa and former world number one Luke Donald of England.
Northern Irishman McIlroy, who clinched his second major title with a stunning eight-shot victory at the US PGA Championship earlier this month, was satisfied with his 69, despite losing momentum after the turn.
"It was good," the 23-year-old said after mixing five birdies with three bogeys. "I thought I played really solid, especially starting off, three under through six.
"Got a little quiet around the middle of the round, and my short game let me down a couple of times. It definitely could have been a few shots better, but I'm happy with how I played."