Wilson, of England, opened with 66. He had six birdies in the first round and seven in the second round.
On Friday, he birdied Nos. 1, 3, 8, 10, 11, 15 and 16. He has yet to make a bogey.
“I played nicely,” Wilson said. “The fact I haven’t had a bogey for two rounds shows I’m playing solidly and sensibly.”
Wilson has nine second-place finishes on the European Tour but has yet to win.
He lost his main tour card at the end of last year after failing to record a top-10 finish and finishing 130th in the Race to Dubai.
It hasn’t been any better this year for Wilson.
In eight starts, he has missed the cut four times. His best finish is a tie for 26th place.
Wilson is at 13-under 131.
Tied for second are Sweden’s Magnus Carlsson (66) and 19-year old Joakim Lagergren (66) and England’s Andy Sullivan (64).
Jamie Elson, another former Augusta State golfer, is nine shots back after rounds of 70-70.
The tournament is being played on a Portuguese archipelago about 400 miles west of Morocco.