Woods went into day three trailing two shots from the lead and at the end of the round was again sharing second place, just one behind 26-year old rookie Canadian Corey Conners.
Tiger Woods was right in front of him during the third round at Innisbrook, and Conners could hear the roars for Woods all afternoon.
An 11ft putt for birdie on the 10th, followed by a smart four on the par-five 11th took him to within two shots of the lead.
Rose had 66 and will be in the final group today with Conners, who has led after each round.
"I don't see it going backward from here", said Snedeker, who played a round with Woods at Torrey Pines and twice at the Honda Classic.
That left the former world number one, who had spinal-fusion surgery last April and only returned to the PGA Tour this year, ahead of some other high-profile players competing this week, including world number four Jordan Spieth (76), four-times major victor Rory McIlroy (74) and Swede Henrik Stenson (74).
Tiger Woods has made such a great recovery from last April's spinal fusion surgery that many might wonder why he did not have the procedure sooner.
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And the 14-time Major victor surged to the top of the leaderboard for the first time since August 2015 before ending the second round in a tie for second, two shots behind leader Corey Conners. "For me, I'm ecstatic to have a chance to play again and to have a chance to win golf tournaments and compete".
Woods got off to a dream start on the 560-yard par-five first hole, reaching the green in three to set up a tap-in for an easy birdie. Even as recently as last fall Woods himself wasn't sure if he would ever be able to play golf again. South Africans Rory Sabbatini (67) and Tyrone Van Aswegen (68), Ryan Palmer (70) and Kelly Kraft (70) are all four back in a tie for seventh to round out the top 10. "I'm getting a little better, piece by piece".
As for the Masters in a month's time, Woods was playing with the favourite to claim the green jacket - and he beat Spieth by nine shots over the course of 36 holes. Woods had scored better in every round until Saturday. On the next hole, the par-4 10th, Woods rolled in a 22-footer for birdie to briefly seize a share of the lead. It all started there for Woods, who clearly feels better than he has in years.
Woods, though, surged back, with a birdie at No. 14, before finishing with four straight pars.
"That was sweet", Woods said.
"Today was a very good test of all the things that I'm trying to implement", Woods said.
"I didn't know I had the sole lead", Woods said. Conners grew up idolizing Woods for his 14 majors and 79 victories on the PGA Tour, and it was hard not to get caught up in so much hysteria.
"We've been hearing it all week", Rose said.