Damian Moore, originally from Portnoo in Donegal, and his Caribbean-born wife Glenda broke down as the casket was taken from the Church of St Rose of Lima in Brooklyn.
A group of New York City sanitation workers -- colleagues of Damian -- formed a guard of honour as the coffin was brought on its final journey and thousands of mourners lined the streets on the way to the church.
A separate car carried the dozens of floral wreaths sent from relatives, colleagues and friends.
The boys were laid to rest in Green-Wood Cemetery in Sunset Park as Damian and Glenda gripped each other's hands, weeping as the casket was carried past them.
"Faith tells us we have two little angels in heaven, but we've lost two beautiful little boys," Department of Sanitation Chaplain Peter Colapietro, who led the funeral, said. "There are no words."
"St Paul tells us that there is nothing that can separate us from God's love, and if we believe that, too, then there is nothing that can separate you and the rest of the family from Brandon and Connor's love," Colapietro told mourners.
"Nothing can separate you from their love."
Guy Victor, whose wife is Glenda's godmother, said it was fitting for the two boys to be buried in one coffin:"Those boys belong together."
Glenda had been trying to bring her sons to safety when the family SUV was overturned by high winds and a wall of water washed the two boys from her arms. Their bodies were later found in a wooded marsh.
Damian was at work in the city as part of the Sanitation Department's emergency response to the superstorm when the tragedy occurred.
As the two little boys were being buried in New York, their grandparents in Portnoo, who were unable to travel to New York, attended a memorial Mass in their local church in Donegal.