Schauffele was the overnight leader having surged top of the standings by three shots, but the four-time PGA Tour victor lost ground on the penultimate day following two birdies and four bogeys.
While 31-year-old Henley was safe all the way and finished it ideal with five birdies, including three in a row that achieved at the beginning of the second half of the game.
He then cooled coming in, but still finished with a bogey-free round. "I made a nice par save on the third hole, just kept staying patient and made a lot of nice putts. But I am just happy I made that par putt on the last", said Schauffele. "It's a tough course but if you hit some good shots you can have some chances".
'I'm trying to do the right things, working hard on my game, working hard on what I need not just for these weeks, but obviously looking ahead to Augusta as well. Two birdies on the front nine were interrupted by a bogey at the seventh but then as he turned for home, he found his form, birdying six of the back nine, including four of the last five.
"Finishing birdie-birdie was nice and hopefully I can take a bit of momentum going into the weekend".
"I've got to play a solid round of golf, keep my head down and keep grinding".
The CJ Cup: Russell Henley opens up three-shot lead in Las Vegas
Henley now holds a 54-hole lead/co-lead for the third time on Tour - the American has converted one of those instances into a victory via the 2013 Sony Open.
After reaching the turn in 34, Henley drained a 25-footer at the 10th and made a tap-in birdie at the driveable next, with the three-time PGA Tour victor making a five-foot gain at the 12th and then finishing his blemish-free card with a run of pars.
"It was kind of a tie".
Hatton couldn't quite keep up with his first seven-under-65-year-old round, but still managed to card a four-under-68 round as 11-under-par. It was just a lot of bad breaks kind of. Rahmbo needs, at least, to finish in second position to regain the world number one, so he has it really raw with a day to go. - Jason Day withdrew on the second hole of the final round Sunday at the CJ Cup with a neck injury.
Second-ranked Jon Rahm of Spain made a 10-foot eagle putt on No. 16 and is tied for 14th after a 68, while 11th-ranked Brooks Koepka, the 2018 CJ Cup champion, is tied for 18th after a 68, and 14th-ranked Patrick Cantlay of Los Alamitos and UCLA stumbled to a 74 and is tied for 51st.