The world No. 1 recovered from a dreadful start to shoot a one-over 72 and finish ahead of only five players in the 99-man field at Boston TPC, the second instalment in the lucrative lucrative FedExCup playoff series.
Woods, currently ranked 65th in the FedExCup standings, needs to finish in the top 70 after the Deutsche Bank Championship to advance to the third round of the series at next week's BMW Championship at Cog Hill outside of Chicago.
"I just didn't have it today," he told reporters. "I wasn't really doing what I was supposed to be doing swing-wise and wasn't releasing the putter blade. It was a bad day all around.
"I'm obviously going to have to shoot something pretty good tomorrow." After crashing to four-over after six holes, Woods salvaged his round amid intermittent afternoon drizzle coming from the outer bands of Hurricane Earl, but conditions were by no means difficult with just a light breeze wafting across the course.
Woods has yet to win this season but had appeared to have found some form after finishing a respectable 12th at the Barclays tournament, days after announcing his divorce from Swedish wife Elin.
Co-leaders Day and Johnson enjoyed playing together in dry morning conditions and notched a combined 23-under with Ryan Palmer in their group.
"We kind of fed off each other," said Day, who compiled 10 birdies. "Coming into this event, I felt very confident with my swing and I just had to work on a few things with my short game.
"The first couple of days I got here, I tried to square my putting up a little bit and that worked out great. Everything kind of clicked." Johnson added: "If you get off to a good start, it breeds momentum. We all birdied the first hole and it fed into the remainder of the day.
"I probably didn't hit it quite as well as those guys (but) I hit it fine and I putted beautifully." Johnson and Day lead a clutch of golfers on 64, including Palmer, Northern Irishman Rory McIlroy and Australia's Geoff Ogilvy.
McIlroy stormed up the leaderboard late with an eagle at the par-5 18th, after landing a sublime five-wood approach 25 feet from the hole and sinking the putt.
