Griffiths stands at 17-under-par 199 for the first third-round lead of his career. Lying two strokes back at 15-under-par 201 are Niclas Fasth, who also fired a 66, and Robert Karlsson, who followed his course-record 63 in the third round with a 68.
Overnight leader Graeme Storm chipped in at the 18th, finishing with a 2-under 70 to fall into a tie for fourth place at minus-14. Thomas Bjorn joined him there after a 68.
After that, 11 players are separated by just three strokes. But they are all looking up at the Englishman Griffiths.
In addition to having the lead, Griffiths, 25, has been perhaps the steadiest player over the first three rounds at San Roque. He nearly finished off his third straight bogey-free round before dropping a shot at the par-3 17th on Saturday.
'I am going to try to keep doing what I am doing,' said Griffiths, who will be looking to become the ninth first-time winner on tour this season. 'I felt very comfortable out there today and hit a lot of good shots again. I just need to get comfortable early on and keep playing how I am playing.'
Teeing off in the final group with Karlsson and Storm, Griffiths moved to 13 under with an eagle at the par-5 second hole. He made the turn at minus-14 after a birdie at six, then went on to play the back nine at 3 under.
After birdies at 11, 14, 15 and 16 -- he has birdied each of those holes twice so far -- Griffiths pulled a 6-iron into the rough at the 215-yard 17th. From an awkward stance, he then chipped short of the green on the way to a bogey four.
'It's a brand-new experience leading, but it will be an interesting day whatever happens and I'm going to give it my all,' said Griffiths, who earned his tour card at last year's Q-school, which was also held at San Roque.
Jose Manuel Lara and Carl Suneson share sixth place at 13 under after rounds of 69 and 70, respectively.
One stroke further back, five players are knotted in a tie for eighth, including defending champion Peter Hanson, who shot a 68. Joining Hanson at 12 under are Philip Archer, Mattias Eliasson, Louis Oosthuizen and Gary Orr.
David Bransdon (69) and James Hepworth (69) are at minus-11, while Jordi Garcia del Moral -- the only amateur to make the cut -- lies one shot further back to share 15th place with Miles Tunnicliff.