Mitchell, who is chasing only his second career title after a 2019 win at the Honda Classic, drilled a superb iron from the fairway from around 150 yards into the hole for an eagle two on the par-four 18th.
That was the final act of a barnstorming finish by the journeyman, who also collected birdies on the 16th and 17th holes to go vaulting up the leaderboard.
Mitchell's eagle on the last completed a five-under-par round of 66, leaving him alone at the top of the leaderboard on 10 under after 54 holes at Innisbrook's Copperhead course in Palm Harbor, Florida.
Three players - Ireland's Seamus Power, Canada's Mackenzie Hughes and Peter Malnati - are lurking two shots off the lead on eight under.
Mitchell's closing eagle came as a surprise to the world No.72, who got something in his eye after making the shot and didn't see the ball land.
"When I looked up something kind of flew in my eye, so I kind of looked away and never saw it come down and land, but I knew when I hit it, I was pleased with the contact," Mitchell said.
"I wasn't going to be able to see it go in the hole anyway, but I didn't even see it come down next to the flag."
Mitchell's lone PGA Tour victory in 2019 came against a top-class field, with Brooks Koepka and Rickie Fowler finishing runners-up by one shot.
At the time, Mitchell believed that breakthrough win would be the first of many. Instead he has endured a five-year drought.
"I think I got my win early and felt like I could win more," Mitchell said. "Unfortunately, that's a really high expectation out here.
"Hopefully, I can continue to work on the right things, maybe even add some more stuff into my practice so that I can just put myself in contention more often.
"The more you're in contention the better chance you have to win."
Mitchell had given no clue that he was ready to mount a charge earlier in his third round.
Two birdies and three bogeys on the front nine left him one over par at the turn, before his round caught fire down the stretch.
He chipped in for birdie on the 12th and then another pinpoint chip on the 14th left him with a short birdie putt which he duly converted before his birdie-birdie-eagle finish.
Power and Malnati stayed in touch with three-under-par 68s to finish the day on eight under, alongside Hughes, who carded a two-under-par 69.
Three players - Cameron Young, Brendon Todd and Chandler Phillips - are three off the lead on seven under.
