Cevaer shot 2-under-par 70 Saturday, while Singh managed a 1-under 71.
The field was hampered Saturday by gusty winds on the course at the London Golf Club.
"I was missing a lot of putts and it was windy," Singh, also a second-round co-leader, noted. "I said (to myself) 'just hang in there.' I had a shaky start, but I covered up with a good finish."
It is the third time in his career Singh has held at least a share of a third-round lead, while Cevaer had never previously held a 54-hole lead after Saturday play.
"I managed to strike a perfect drive (at the 18th hole)," Cevaer said. "That's brilliant for me."
Putin thinks Obama would save him if he were drowning
The Giudices celebrate Easter as they prepare for jail