Woods made a chip-in birdie on the ninth to grab a share of the lead at 7-under, but Conners responded with a pair of wonderful wedge shots as he made the turn to jump back on top of the leaderboard.
While Woods has won 79 times, he hasn't been in the winners circle in almost five years-his last win was at the 2013 WGC-Bridgestone Invitational.
"Loud as I've heard it in a long time", Snedeker said.
Woods followed with a birdie at the 10th, but he failed to convert from short range at the par-5 11th.
Playing behind Woods on Saturday didn't seem to faze him, either.
"It feels like it's back to "12 or "13", said Joe LaCava, Woods" caddie since 2011".
"I'm excited", Woods said.
"I keep getting a little bit better, here and there making little subtle tweaks and I've done that from tournament to tournament", the 14-times major champion told reporters. "I was really patient out there, hit a lot of good tee balls and picked my shots to be aggressive at some pins". I was hoping something to take the pain away, I should get up out of bed and walk again.
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He drained a putt from 22 feet for birdie at No. 10 underneath an overcast sky similar in color to his dark gray slacks and cap, contrasting Woods' bright pink Nike shirt that helped him stand out in a crowd even more than normal.
Tiger Woods has played consistently well for seven consecutive rounds.
The galleries swelled with each hole, and among the constant, predictable chatter and screams came an occasional cry of "I love you, Tiger", from the mouths of women, men and children alike. But this was the first time he has holed a shot from off the green this year. I've got a shot going into tomorrow. He said his doctors had not given him clearance to hit balls.
"I got into the field late, and kind of came in here with nothing to lose", he said.
Woods would falter with a final-round 70, finishing four strokes behind victor Davis Love 3rd, and less than a month later would have the first of two back operations that would keep him away from competitive golf, with a couple of exceptions, until January of this year.
By rule, Cousins' bag was considered an obstruction, which allowed him to take a free drop.
Conners will be paired with Justin Rose in the final round and will tee of at 2 p.m. Sunday.
Watch the final round of the Valspar Championship live on Sunday from 5pm on Sky Sports Golf and 6.30pm on Sky Sports Main Event.