Olesen made six birdies to finish with an overall 15-under 273 at Verdura Golf and Spa Resort for his first career victory on the European Tour.
Wood picked up five shots in his first five holes -- including an eagle on the par-5 fourth -- and tied for the lead when Olesen bogeyed after hitting a wild approach shot to the 13th green.
But the 22-year-old Olesen, who led by three shots overnight, recovered with a birdie on No. 14 and finished with four straight pars.
"I played solid all day and I'm happy with that," Beem said. "It really felt good to play well again."
It was the first time in four events that Beem has made the cut on the European Tour.