Arguably the best player on tour yet to break through for a victory on golf's most prestigious tour, Fleetwood fashioned a brilliant bogey-free round of 63 to surge to 16 under for the tournament.
The Englishmen started the day in a share of the lead with superstar Americans Justin Thomas and world No.1 Scottie Scheffler, one shot of ahead of Australian Day.
But in extraordinary, million-to-one scenes, Scheffler and Thomas racked up disastrous triple and quadruple bogeys respectively in their rounds to crash out of contention.
Instead fellow Americans Russell Henley and US Ryder Cup captain Keegan Bradley emerged as Fleetwood's closest pursuers at the end of a most dramatic moving day at TPC River Highlands.
Henley amassed nine birdies in his own blemish-free round of 61, while Bradley matched Fleetwood's 63 to also finish three shots behind the hot pacesetter.
Day followed up two 68s with a 69 to be two strokes further back in solo fourth spot entering championship Sunday.
The former world No.1 looked to have slipped out of contention with two mid-round bogeys before conjuring a hat-trick of birdies from the 13th to 15th holes to give himself a shot at claiming a 14th PGA Tour victory.
With US trio Brian Harman (65), Wyndham Clark (66) and Harris English (67) next best at eight under and eight shots off the pace, it looks a race in four to the $US3.6 million ($A5.56 million) winner's cheque.
Fleetwood, though, will take some catching.
The Paris Olympics silver medallist has his best chance yet to clinch a maiden Tour triumph following a record 41 top-10 finishes without a win, the most in 52 years.
After ambling along for much of the first two days, Fleetwood has played his last 24 holes in 12 under, reeling off three eagles and six birdies in an electrifying stretch to seize command at the $US20 million ($A30.9 million) event.
Eyeing a fourth victory in six starts, Scheffler was the clear favourite entering Saturday's third round (Sunday AEST) level with Thomas and Fleetwood at nine under.
But the PGA champion dropped three shots on a diabolical opening hole, and never recovered.
Scheffler 's third-round 72 left the triple major champ in a five-way tie for eighth at seven under, nine shots adrift of Fleetwood, with Rory McIlroy (67), Lucas Glover (68), Patrick Cantlay (68), Nick Taylor (69) and Danny McCarthy (70).
Thomas is another shot back at six under after racking up a nine on the par-5 14th hole.
Day's fellow Australian former world No.1 Adam Scott rebounded from his final-round horror show at last week's US Open with a sizzling round of 62 to rocket 34 places up the leaderboard to a share of 25th at four under.
