The 26-year-old Spaniard finish at 19-under 269 at the Doha Golf Course after a round that included seven birdies and four bogeys.
Winning is not easy, Quiros said. It is easy for guys like Sergio Garcia and others who win so often. So, definitely it is a big surprise for me to win here.
Oosthuizen shot a 71 and Stenson had a 68 that included an eagle on No. 10. Damien McGrane (67) was fourth, another three strokes behind back.
After a shaky start, Quiros righted himself on the back stretch, getting birdies on Nos. 16-17 to seal the victory.
It wasnt a perfect day, he said. I took time to get going. It is a surprise to win here.
Quiros became the first Spaniard to win the Qatar Masters title in the 12-year history of the tournament, and earned $416,660 for his victory.
Miguel Angel Jimenez (69) finished in a tie for fifth with Maarten Lafeber (72), both at 276. Andrew Coltart (72) was a further stroke behind, along with Garcia (70).
The European Tour stays in the Middle East for the third straight week, next heading to the United Arab Emirates for the Dubai Desert Classic.