Funk had eight birdies and two bogeys for the second-best round of the day and stands at 15-under 195 overall. He has held at least a share of the lead after each of the first three rounds.
'It would be nice to go wire to wire. That's what I would love to do,' Funk admitted. 'I just have to play well.'
Argentina's Jose Coceres shot a 65 and is alone in second place at 13-under 197. Australian Peter Lonard (67) and second round co-leader Cameron Beckman (69) are three shots further back at 200.
Funk will be seeking his eighth PGA TOUR victory and first since the 2005 Players Championship. He is a career 5-6 when holding a 54-hole lead on the PGA TOUR.
On Saturday, Funk opened his third round with a birdie at No. 1 despite aggravating a back injury on his tee shot, which drifted right.
'[I] just felt this nerve pain going right down my butt and down my leg and I knew I was in trouble,' Funk said. 'I was favoring it all day, then it got really bad on a couple of holes.'
So bad, in fact, that a trainer had to come out and work on Funk's back after he made a bogey at No. 12 to fall to 12 under par.
Battling back problems for the first time, Funk pulled himself off the ground and made consecutive birdies at the 13th and 14th and another at the 16th to secure his two-shot lead.
If he wins, maybe he should share the $630,000 prize with the trainer.
'He did something. He pressed so hard on the one part where it was bothering me and I felt something pop a little bit,' Funk said. 'I don't know if it was my hip or his thumb, but it definitely helped.'
Funk is staring at some history.
He will be 50 years, eight months and 11 days old on Sunday. Only five players have ever won a PGA TOUR title after their 50th birthday: Sam Snead (52); Art Wall (51); Jim Barnes (51); John Barnum (51) and Craig Stadler (50).
If he holds on, Funk would move ahead of Stadler to become the fifth-oldest champion in PGA Tour history (Stadler was 50 years, one month and 18 days old when he won the 2003 B.C. Open).
Stadler is also the only other player who has won an event on the Champions Tour and PGA TOUR in the same season, doing it in back-to-back weeks at the 2003 Ford Senior Players Championship and B.C. Open.
Funk won his second Champions Tour title at Turtle Bay last month. Things will be easier Sunday if the back pain subsides.
'Hopefully it's not going to be a big deal tomorrow. I don't want to dwell on it,' Funk said. 'It's just something we deal with out here.'
Boo Weekley, who shared the overnight lead with Funk and Beckman, had a 70 on Saturday and fell into a tie for fifth place with Skip Kendall at 9-under 201.
Kendall fired the round of the day at El Camaleon, a 7-under 63, to move up from a tie for 49th place overnight.