Woods, who has not scored a tournament victory since August 2013, needed a birdie on the par-four final hole to finish level with eventual victor Paul Casey.
Casey charged from five strokes behind in the final round to overhaul Woods and Patrick Reed by one shot in a compelling finale at the Innisbrook Resort in Palm Harbor.
Woods was two behind with three holes to play - Copperhead's so-called "Snake Pit" - but holed from 40 feet for an unlikely birdie on the 17th and had a similar distance on the last to force a play-off.
Woods hasn't been in this good a position to add to his total since he finished tied for 10th at the Wyndham Championship in August of 2015, and he hasn't lifted a trophy since the 2013 World Golf Championships Bridgestone Invitational.
Woods has to wait at least another week, with the next stop at a golf course Arnold Palmer built and Woods used to own.More news: Toys 'R' Us considering closing United States stores
'I'm looking forward to it [the Masters] and I haven't played Bay Hill in a few years.
"It was one of those days where I just kept getting the half-club, just one of those days where I couldn't quite get the full-club", Tiger said after the 18th.
Casey had four birdies and a bogey on his front nine, then seized control with three birdies on the trot at 11, 12 and 13 that moved him to 10-under.
Woods has won 79 times on the PGA Tour and victory on Sunday would bring him within two of all-time leader Sam Snead.
Woods, now up to 43rd on the FedEx Cup standings, said he would take major confidence away from his best overall display of the year. Last week, 47-year-old Phil Mickelson won for the first time since 2013.More news: Megan Markle's secret baptism with water from Jordan River
Speaking to Sky Sports following the Valspar Championship, Woods said: 'It was a very good week, I feel like I improved [from last month's Honda Classic]. That putt was good for a birdie, pulling him within one entering the 18th hole.
"A couple of putts here and there and it could have been a different story". It's exciting to have him back for the casual golf fan, but now the true Tiger fan gets excited. I said a couple of times if I don't win this thing, I actually want Tiger to win it.
With the 42-year-old making the flawless read and then executing; his ball curled deliciously into the centre of the cup as the gallery went berserk. After he birdied the first hole to pull into a share of the lead with Woods at 9-under par, Snedeker exploded, finishing with an ugly 78.
"I played great golf". Or you can think it's incredible that in such a short time he has clearly demonstrated he's essentially all the way back.
He dropped his only shot on the next hole when his tee shot sailed over the green into matted, thin grass where the gallery had been standing.More news: Russian Federation won't accept meddling in its domestic affairs - Putin
'It's hard to time that when you're having to use your hands more than you should.