The 32 year old Northern Irishman, whose only previous European Tour title also came on Portuguese soil, birdied the eighth in his only deviation from par to move to ten under for the week.
Overnight joint-leader Jamie Elson had a more varied scorecard, the Englishman mixing three bogeys and two bogeys as he slipped back to eight under.
England's Chris Gane and Scots Lloyd Saltman and Alastair Forsyth were still in the running at seven under.
Earlier in the day Simon Wakefield broke the Porto Santo Golfe course record with a magnificent 63.
The Englishman briefly threatened the first 59 in European Tour history - but needing to pick up two shots in his last two holes he parred the 17th and double bogeyed the par five last.
"I've been threatening to play well for the last few weeks, then yesterday on the range I just found something I felt comfortable with, I had another good session on the range this morning, and took it out onto the course with me," said Wakefield.
The European Tour Qualifying School winner had only registered two bridies on the front nine all week, and starting the day eight over par had no chance of challenging for the title.
But he eagled the third, then reeled off four birdies in a row from the fifth to turn in 30.
Four birdies in the first five holes of his back nine set up the possibility of a 59, and a further gain at the 16th made it likelier still.
"I was in last place, so I just decided to relax and be aggressive because I had nothing to lose," he added. "I got off to a great start with the eagle on the third, and just kept the momentum going for the rest of the round.
"It was flawless golf - I don't think I hit a bad shot all day, even on the last. My tee shot was down the right but not in any trouble, so I decided to lay up and left myself the perfect wedge. The wind was coming from the left, but it started to draw a little bit into the wind, caught the bank and ended up in the water.
"So to shoot 63 with a seven on the last was pretty good going, but it could've been an outstanding round so it's a slightly bitter pill to swallow.
"I was nine under after 12, and I'd played the last six holes all week. Then I birdied the 14th and drained an absolute monster on the 16th from about 60 or 70 feet which was just comical really, because at that point it didn't really matter what I looked at - it just went in.
"I hit it to about 20 feet on the 17th, and I thought to myself that if I could roll that in, I'd give myself a chance. But when I missed that putt, it went out of my mind really - I was just concentrating on staying on 11 under. But then obviously my stomach sunk after what happened on the last. But it's obviously given me a lot of confidence and hopefully I'll get an invite to the BMW PGA Championship next week on the back of it."