The 27-year-old Wiesberger, bidding for his third title of the season following victories in his homeland and South Korea, picked up six birdies in seven holes from the eighth to fire a six-under-par 65 for a 13-under aggregate of 200.
Overnight leader Ross Fisher (69) was in second place, three strokes ahead of fellow Englishman Richard Finch (66), former U.S. Open champion Michael Campbell (67) of New Zealand and Ireland's Shane Lowry (67).
European Ryder Cup vice-captain Miguel Angel Jimenez (68) was also on the fringes of contention on eight-under 205.
"After seven holes I was not thinking about a 65," Wiesberger told reporters on the Algarve. "I hit some horrible wedges early on but I grinded through that and hit better shots around the turn.
"I then played beautifully on the back nine and my score could have been even lower."
- Ross Fisher