Santos, who was four shots behind third-round leader Carlos Del Moral entering Sunday's play, put on a charge that netted him a bogey-free final round that featured nine birdies.
He finished at 22-under 266 for his first European Tour victory -- two strokes better than the previous Madeira Islands Open record.
Santos easily outdistanced second-place finisher Magnus Carlsson, who fired a 5-under 67 to end at minus-18.
Andreas Harto, who also carded a 67, claimed sole possession of of third place one shot further back.
Del Moral, meanwhile, stumbled after Saturday's 63 to grab to a 73, finishing in a fourth-place tie at 16-under.