Vast galleries arrived early to TPC Sawgrass to greet Woods and Mackenzie Hughes on the first tee at 9am, and the two-time champion made the ideal start with birdies at the opening two holes. The most impressive shot of his day (and possibly the one that shut down this tournament) came on the par-5 11th.
There is another Australian-held record Simpson can surpass on Sunday - Steve Elkington's seven-shot triumph in 1997 is the biggest victory margin at golf's unofficial fifth major. He tapped in for birdie.
The duo ended their rounds almost 90 minutes before overnight leader and fellow American Webb Simpson was set to tee off leading by five shots at 15-under par. He is 12-under for the tournament, seven shots back from Simpson.
Now Simpson will go for the all-time scoring record of 24-under 64 set by Greg Norman in 1994.
Patrick Cantlay (68), South African Charl Schwartzel and New Zealander Danny Lee (both 66) were a distant second on 10-under, while Tiger Woods (71), at one-under 143, made the cut with nothing to spare, as did Jordan Spieth (68) and Justin Thomas (70).
Woods picked up another shot at the ninth to turn in just 30, and he then birdied 11 and 12 to vault into the top 10 - eight under for the round and in with a great chance to break the course-record of 63.
"I felt like everything was working today", Simpson told Golf Channel after his round. "If it's windy tomorrow like it was today and you're not very sharp, you're going to struggle around here". Alex Noren (69), Charles Howell III (67) and Chesson Hadley (69) are tied at 9-under and 2016 Players champion Jason Day (67), PGA Tour Champions member Steve Stricker (69) and 2017 Tour Championship victor Xander Schaffele (68) are at 8-under. "With these greens as soft as they are, I didn't take advantage of the opportunities I had today to really shoot a good number". Other than Simpson, few players were able to make any meaningful movements, as evidenced by the fact that when Woods signed his scorecard before the leaders had even teed off he was in eighth place.
"I wish I knew what was the difference, [but] I don't know [why]", Woods said.
"Eventually I was going to put all the pieces together and today for the most part I did that", said Woods.
He added: "I wish I could repeat it more often but, honestly, it was just [about] a better start".
Fellow Raleigh native Chesson Hadley entered play Saturday at 9-under but finished with a 2-over 74 Saturday and sits at 7-under heading to Sunday.