"I made some great putts out there today including getting off to a better start than I have most of the season", he said.
He drained the five-foot (1.5 metre) eagle putt and then added birdies at the 18th (his ninth), first and seventh before his first mistake of the day led to a bogey at the par-3 eighth.
Though he has not won since 2013, Woods missed much of four seasons with a chronic back injury before surgery previous year alleviated the problem.
Woods was just as hot as he opened his round by shooting a 29 on his front nine. I think with the way the conditions are, especially with the rain that's forecast, I can't see the scoring being any different. His only bogey came at the par-3 eighth, by far the most hard pin on the course.More news: British Airways investigating data breach from 380000 card payments
Woods made four birdies and an eagle and by all accounts looks really good after his first nine holes of the day.
The 14-time major victor Woods and McIlroy have a one-stroke lead after both shot eight-under 62 which marked the American's best PGA first round since the 1999 Byron Nelson Classic.
Jordan Spieth couldn't keep it in play off the tee and didn't get under par until his 15th hole. He birdied three of the last four for a 67. The crowd was much thinner for McIlroy, but those fans saw quite a show.More news: Ronaldo, Modric, Salah shortlisted — FIFA's best player
McIlroy opted to miss The Northern Trust a fortnight ago as he felt he needed to put in extra work on his wedge play, and he was satisfied that his time on the range was starting to pay off, while his driving was also more accurate than in Boston last week.
But McIlroy threatened to trump his rival with a round that included a career-best six birdies in a row - before bogeying his 16th and 17th holes.
"You don't get many opportunities to break 60 and today was one of them", he said. "I'm not going to say it stings too bad because I'd much rather shoot 62 today and win the golf tournament Sunday than shoot 59 today and maybe not win".More news: India, US discuss trade, defence, visas, oil in first '2+2' dialogue