Woods posted two outward half bogeys and two inward nine birdies in a level par 72 to remain at four under par.
But he is now seven shots behind the leading 36-hole duo of Henrik Stenson (69) and Bryson DeChambeau (66) on 11-under.
Still, the bookies think Woods is still well in the hunt and they make him a 16/1 shot to come out on top.
Stenson added a second round of 69 to his opening 64 at Bay Hill on day two to set the clubhouse target on 11 under par, a target matched minutes later by DeChambeau following a 66.
Rory McIlroy, who has missed the cut in two of his last four starts on the PGA Tour, sat six shots off the pace after a second round of 70 which featured five birdies and three bogeys.
Woods was a shot further back after two birdies in his last seven holes saw the 14-time major champion finish where he began.
Stenson had covered the back nine in 31 on Thursday, but after starting from the 10th on Friday, the former Open champion could only manage nine straight pars to reach the turn in 36.
The par streak was extended to 13 holes before Stenson found his range on the greens to birdie the fifth, sixth and seventh to maintain his bid for a first win of the season.
Asked what made the difference between missing the cut in last week’s Valspar Championship and his performance so far, the world number 15 told PGA Tour Live: “Putting more than anything, but a combination of putting and my shots.
“I’ve been hitting a few really close this week and setting up some good opportunities from three or four feet. Today wasn’t as good as yesterday, obviously, but the important part for me was 16, 17, 18. I scrambled for par all those three holes after hitting some not-so-good golf shots.
“I kept patient and then I got on a strong run and made three (birdies) in a row coming home. Three under around this golf course is never bad.”
McIlroy’s putting was noticeably better than in recent weeks and the four-time major winner told Sky Sports: “That’s been a huge improvement over the first two days.
“I sort of messed around on the putting green a little bit, trying to go back to some feels I’ve had before and putted really well. Hopefully that continues.
“Over the weekend last year I was hitting driver pretty much everywhere, leaving myself wedges in. If I drive it like that again over the weekend I feel like I’ll have a good chance.”
McIlroy shot weekend rounds of 65 and 69 last year to finish in a tie for fourth, two behind winner Marc Leishman.
Woods bogeyed the first after hooking his tee shot into the trees and had a superb short game to thank for saving par on the second and third, before a wild tee shot on the fourth fortunately hit the out-of-bounds fence and stayed in play.
The 14-time major winner three-putted the ninth for a second bogey of the day but birdied the 12th and 16th and narrowly missed from 15 feet for another on the last as he seeks a first victory since 2013.
Source : EXPRESS