Former world number one Woods, who had spinal-fusion surgery last April and only returned to the PGA Tour this year, made his only bogey of the day on his final hole for a three-under-par 68 at Innisbrook Resort's Copperhead course.
Woods shot a 67 on Saturday. Conners will play out of the final twosome with Justin Rose.
Woods will surely fancy his chances of claiming his 80th PGA Tour title on Sunday, with unheralded rookie Conners - who again impressed with a 68 - the only man above him on the leaderboard.
And while Woods gave an encouraging report about his future health last September when he served as an assistant for the U.S. Presidents Cup team, he also cautioned he had no idea if he could play golf, let alone compete at the highest level.
That saw Woods, 42, who is looking for his first win in nearly five years, card a second-round three under par 68 in the Valspar Championship in Florida.
This will be the 70th time Tiger Woods is at/within 1 of the lead after 54 holes on the PGA Tour. Obviously it's not. I really remember that and all those good feelings.
Snedeker, who returned from his own injury (rib cage) last fall, is trying to make the Masters field either by winning here or by moving into the top 50 in the Official World Ranking the week of the year's first major.
"I didn't want to go there".
Speaking on Sky Sports, Woods said: "I had a good time".
And the 42-year-old took full advantage by finding a greenside bunker with his approach, splashing out to four feet and holing the birdie putt to take the outright lead. "It kind of feels like you're playing in a major championship in a normal round, which if anything should bring out better golf for me". At just about that time a collective sigh of relief could be heard from everyone with a weekend pass.
"It was really cool", the wide-eyed, smiling Canadian said.
"Came out and tried to have as much fun as possible", Conners said. Then on the par-5, fifth he hit his sand shot to four feet for an easy birdie.
"I don't want to get carried away from one good tournament, but you could see signs of him playing well and hitting it better, so, no, I'm not surprised". Get your free 2-week Foxtel Now trial & start watching in minutes.
Entering the day, Woods' third-round scoring average on Tour dating back to 1992 was 69.6 - best among players with a minimum of 37 rounds.
Birdies at the ninth and 10th followed but he stalled briefly after a bogey four at the par-three 13th.
Spieth missed the cut for the second time this year. I made that one. A bogey on No. 16 left him at 9-under.
"It feels like it's back to "12 or '13", said Joe LaCava, Woods's caddie since 2011".