Cevaers birdie, only the second on the wind-swept final green in the third round, gave him a 70 that put him at 9-under 207. Singh, the overnight leader, made birdies at four of the last six holes for a 71 after struggling with five bogeys on the first 11.
Rory McIlroy of Northern Irleand finished strongly for a 68 that gave him a share of third place with Chris Wood (68) of England and Alvaro Quiros (69) of Spain at 6-under 210.
Cevear set up his final birdie with a strong approach after a perfect drive.
Its a great feeling when those shots come off like that, perfect, said Cevaer, who had three birdies and one bogey in his round. Im happy to be swinging well and I enjoyed it very much.
Singh struggled through the early holes in the breezy conditions on a course with deep rough.
Its almost a U.S. Open setup, he said. At the fourth hole I was in deep rough with a lob wedge in my hand, and moved the ball just six inches.
But he birdied the 13th after a fine drive, the 14th with a 20-foot putt and the long 15th with a chip to three feet. Then he saved his best shot of the day for the 225-yard 17th.
It was a 3-iron cut against the breeze, he said. Then I made a 15-footer for the birdie.
McIlroy had three birdies and an eagle over the first 13 holes, bogeyed the 14th but finished strongly with four straight pars.
You have to make your score on the front nine with four of the first holes playing downwind. Then you hang on, he said.
Sergio Garcia was one of many to make a triple-bogey seven at the last hole, finishing with a 74 for a share of 47th.
Pablo Larrazabal (79) of Spain was in last place after taking a nine on the par-3 17th. His tee shot landed in a bush and he had two penalty drops and a whiff left-handed before holing a 9-footer.
It was a good nine, he said.