Overnight leaders Stenson and Rafael Cabrera-Bello started the day on 14-under, three strokes clear of England’s Justin Rose, with four players including world number one Rory McIlroy a stroke further back.
As the turn approached, Swede Stenson and Spaniard Cabrera-Bello were a further stroke ahead and they seemed set for a straight shootout before nerves got the better of them.
Stenson bogeyed the eighth and dropped two more shots at the 11th after shanking an iron out of bounds as Cabrera-Bello, ranked 104th in the world, led with three holes to play despite a 12th hole bogey.
“I’m exhausted,” Stenson told reporters. “On the back nine I didn’t play my best. I had a shocking hole 11. That kind of put me back.”
Cabrera-Bello’s golf veers between brilliant – his second round 64 was the tournament’s best – and lamentable. The latter trait became apparent as he found water at 16 and 17, dropping four shots on another sweltering desert day.
McIlroy and Rose, almost unnoticed, had closed to 14-under to tie with Stenson.
Rose, 34, made up six shots in nine holes on Stenson and Cabrera-Bello as the former U.S. Open champion birdied 14-16, while McIlroy sunk four birdies to be back in contention for a title he appeared to have thrown away with successive double bogeys on Saturday.
The Northern Irishman rued three lip-outs on the final-round front nine, but was fortunate on the 18th when his tee-shot hit a rock by the water and bounced 30 yards on to the fairway.
He then luckily hit the grandstand behind the green, but fluffed an eight-foot birdie chance.
Meanwhile, Stenson – the player his rivals refer to as “Ice Man” – landed a tee-shot on the par-three 17th within a foot of the pin. He converted that for 15-under and birdied the next to end on 272 to clinch the $1.33 million first prize.
“On 17, it was good for a five‑iron. I hit a nice shot pretty much straight at it coming in off the left,” added Stenson.
McIlroy (68), Rose (69) and France’s Victor Dubuisson (68) were joint-second on 274.
Stenson’s win put him second on Europe’s money list – McIlroy was crowned champion last week – and he will earn a further $800,000 from a $5 million bonus pool shared among the Tour’s top 15 players.
(Editing by Ed Osmond)