Woods parlayed his 54-hole lead into victory in 2005, but he has not since added to his collection of four Green Jackets, despite coming close several times in the ensuing decade-plus.
He will start Sunday's final round joint second with fellow American Tony Finau, while Molinari will be the man to catch at 13-under 203.
The Italian is unlikely to be intimidated, after staring down and overtaking Woods en route to winning last year's British Open at Carnoustie, where they were paired in the final round.
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A victory on Sunday would be Woods' fifth, leaving him second behind six-times champion Jack Nicklaus.
Arnold Palmer also had four victories.
Woods has been stuck on 14 major titles since the 2008 U.S. Open, and the early holes on Saturday offered little inkling of the fireworks ahead.
Four pars followed by a bogey at the difficult newly-lengthened fifth left him languishing at five-under-par.
For a time he failed to join the birdie party in benign condition on a course where marshmallow greens allowed for players to fire fearlessly at the pins.
But a 20-foot birdie at the sixth sparked his round as the 43-year-old quickly climbed up the leaderboard by picking up further shots at the next two holes.
Not that he was perfect over the middle holes.
He pushed his drives at the par-four ninth and 11th holes, but both times fortunately found a clear opening and had no trouble threading a recovery between the Georgia pines and saving par.
But his biggest piece of luck came at the par-five 13th, where he hooked his drive so far left that the ball seemed more likely to end up in adjacent Augusta Country Club than stay in Augusta National. But it hit a tree and fell to earth right of Rae's Creek tributary, in the clear in light rough.
He took advantage of the break, punching his second shot to wedge range and then skipping his next up to set up a birdie.
Further birdies followed at the par-five 15th and par-three 16th.
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