There were some incredibly low scores around TPC Summerlin on Saturday, with Cantaly carding a sizzling 60 while Kim signed for one of two 62s as the duo moved to 19 under for the tournament, three ahead of the chasing pack.
Cantlay's putter was red-hot, rolling in five birdies in his opening six holes, then another five on the back nine. On the last, the American had a 25-footer to break the magical 60, but he played the ball too high of the cup.
"I hit good putts all day today," the world number four told pgatour.com.
"You can't make every single one as much as you'd like to. I'm very happy with how I played, and I'm in a good spot going into tomorrow.
"Same game plan as the first three days, and it's going to take a low one again tomorrow. This golf course yields low scores, and I expect the same tomorrow. Everyone will be gunning for me, and I've got to shoot a low one."
Meanwhile, Kim finished in style, firing his wedge to within two feet of the hole on the last for a simple birdie - his ninth of the day - to tie for the lead.
"I took care of what I really needed to take care of on this golf course and just needing a good round to give myself a chance on Sunday," said the South Korean, who is yet to card a bogey or worse this week.
"I'm really happy with myself just keeping it tight. This course is very, very scorable so you've got to play good golf. You've got to make a lot of birdies. Anyone is in this really. It's not just me and Patrick. There's a lot of guys who can still play well and win it."
Tied for third on 16 under are Matthew Ne Smith and Chilean Mito Pereira, while defending champion Sungjae Im is lurking on 15 under, four shots off the pace.