"I was dreaming just to run in New York City. The dream has come true this morning," Gebrselassie said.
"Wow, I'm so happy!" Hilda Kibet of Kenya won the women's race in 1:10:32, out sprinting defending champion Catherine Ndereba by 1.15 seconds.
Nina Rillstone of New Zealand, who led until the final 500 metres when the two Kenyans passed her, finished 2.60 back in third.
For the men, near the 13-kilometre mark, the Somalia-born Abdirahman surged ahead to leave Cheruiyot behind, and then Gebrselassie left Abdirahman in his wake for the final eight kilometres of the 21-kilometre race.
"I thought I was going to recover my surge and then just maintain the pace but it wasn't that way," Abdirahman said.
"I didn't give up, no way. We know Haile's the greatest, but at the same time, this is sports."
Gebrselassie appeared in complete control as he ran alone down the West Side highway.
The temperature in Central Park was 21 degrees Celsius after a week of oppressive heat and humidity in the Big Apple.
Cheruiyot was taken to a hospital as a precaution after he finished in 1:00:58. In October, the Kenyan slipped while crossing the finish line of the Chicago Marathon and spent two days in the hospital with a concussion.
Gebrselassie, who has won three marathons in the past two years, won gold in the 10,000 metres in Atlanta in 1996 and Sydney in 2000.
His time was the second-fastest half marathon run in the United States, second only to his own 58:55 in Tempe, Arizona, last year.