The Australian carded a five-under-par 65 on Saturday, the low round at Sawgrass Country Club, to move from a share of first at the halfway point to solo leader after round three.
Only the top five and ties get PGA Tour cards after the fourth round.
Endycott is striving to regain full status after finishing 139th in his rookie PGA Tour season this year and was exempt into the final stage of Q-school.
He opened the event with the only bogey-free round at TPC Sawgrass' Dye's Valley Course on Thursday, a five-under 65, and has followed up with rounds of 68 and 65 at Sawgrass Country Club.
The 27-year-old has recorded just one bogey through 54 holes and is the only player in the field with fewer than four scores of bogey or worse through three rounds.
"It's been really solid this week," Endycott said.
"(I've) really been working hard on limiting mistakes. Just did a really good job of that today. I didn't really make a mistake today on a tough day."
With all golfers playing both courses twice, Endycott will finish at the Dye's Valley Course on Sunday (Monday AEDT) having converted his only 54-hole lead in PGA Tour-sanctioned play into victory at the 2022 HomeTown Lenders Championship.
At 12 under, Endycott is two strokes clear of Blaine Hale Jr, with fellow Americans Trace Crowe and Spencer Levin a further two shots back in a share of third.
"I've got a two-shot lead in a regular golf tournament, and trying to close it out," he said.
"There's a lot of good players this week. I've still got to go and play well. I can't go and shoot nothing and expect to win.
"It's one of those ones where I'm still trying to mentally feel like this is a Sunday of a PGA Tour event. It's what you work for.
"I just want to go do my best tomorrow and see what happens."
Endycott's countryman Tom Power-Horan shot a third-round six-under 64 at Dye's Valley Course to surge into a tie for 24th entering the final round.
He remains five shots outside the top five and will need a super-low final round to scrape in.
The other Australians are well back, with John Lyras tied for 68th at one over, David Micheluzzi sharing 111th at five over and Brett Drewitt nine over in joint 137th spot.
Rhein Gibson withdrew after falling back to five over with a third-round 73 at Dye's Valley Course.
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