Former British Open champion Louis Oosthuizen led by two at the start of the final round, but stumbled to a 3-over 75 to slide into third place at minus-14.
Oosthuizen bogeyed the second and double-bogeyed the fifth. He stumbled to another double at the eighth and followed with bogeys at nine and 10. He was all the way back to 11-under at the time. Oosthuizen fought back into contention, but it wasn't enough.
Mahan birdied the ninth, and when Carl Pettersson dropped a shot on the 10th, Mahan was alone in the lead. Mahan extended his lead with a birdie on the 10th, then he held off Pettersson down the stretch.
Rory McIlroy returns to action this week in preparation for The Masters. He lost his spot atop the world rankings with Tiger Woods' win Monday at the Arnold Palmer Invitational.
The field includes 11 of the top 25 from the world rankings.
Golf Channel will have coverage all four days. Their coverage on Saturday and Sunday will be early, before they hand off to NBC for the rest of the round.
The PGA Tour remains in Texas next week for the Valero Texas Open, where Ben Curtis won by two shots last year.
TROPHEE HASSAN II, Golf du Palais Royal, Agadir, Morocco - The European Tour moves a little closer to continental Europe with a trip to Morocco this week.
Michael Hoey struggled to a 2-over 74 in the opening round last year, but went 19-under par over the final three rounds to earn a 3-stroke win over Damien McGrane.
The victory was Hoey's fourth on the European Tour.
In the final round last year, Jamie Donaldson fired an 11-under 61 to set a new course record. Donaldson, along with Hoey and McGrane, will be back in the field this week.
The Molinari brothers, Edoardo and Francesco, will also be at Golf du Palais Royal this week along with Rhys Davies and David Horsey.
Golf Channel will have coverage all four days.
After a two-week break, the tour finally lands in Europe with the Reale Seguros Open de Espana, where Francesco Molinari won by three last year.