Morrison, who is looking for his first European Tour win, upped his lead from one stroke to three over Scotland's George Murray at 18-under 198.
Murray fired a 68 and kept his grip of second at 15-under 201, while England's Oliver Fisher (65) lurked three strokes further back at 204.
The only other player within striking distance of Morrison was Ireland's Simon Thornton, whose 71 on Saturday placed him fourth at 11 under 205.
The only golfer playing in Portugal ranked in the top 150 -- No. 147 Richie Ramsay -- was far from the top of the leaderboard, tied for 64th place at 21 shots back after carding a 76.
Morrison, 25, did much of his damage on the back nine, collecting six birdies and three pars there after shooting a seven-under 29 on the holes Friday.
Swim Week Miami Beach 2014 [PHOTOS]