Dolours’ sister, Marian, who is in prison accused of dissident republican activity, was not at the service.
Rea and the couple’s sons Danny and Oscar helped carry the coffin from St Agnes Church in Andersonstown, west Belfast.
At the graveside in Milltown Cemetery in west Belfast, socialist Eamon McCann told the crowds who were huddled under umbrellas: "If Dolours had a big fault, it was perhaps that she lived out too urgently the ideals to which so many others also purported to be dedicated.
"She was a liberator but never managed to liberate herself from those ideas.
"Sometimes we are imprisoned within ideals; sometimes in war atrocious things are done; sometimes hard things have to be done.
"Sometimes it is very difficult to handle the hard things that you felt compelled to do when you are soft-hearted at the core of your being. And Dolours was a soft-hearted person as well as a hard person in her politics."
Price, 62, was an unrepentant republican hard-liner who fell out with Sinn Fein after the party endorsed the Northern Ireland peace process, encouraged the IRA to give up its guns and embraced power-sharing with unionists at Stormont.
She was found dead at her home in north Dublin last week.
The former wife of actor Stephen Rea, she was convicted and jailed along with her sister for the 1973 car bomb attack on London's Old Bailey courthouse in which one man died and more than 200 people were injured.
Marian Price, who is in jail accused of dissident republican activity, did not attend her sister's funeral. She had been granted several hours compassionate leave to attend the wake yesterday.
Up to 500 people packed into St Agnes' Church in Andersonstown, where books of condolence had been placed in the doorway.
Father Raymond Murray, who was a prison chaplain at Armagh jail and officiated at Price's wedding, told mourners the two sisters had been like bosom twins.
He added: "Their mother never saw Dolours or Marian back in Ireland. They did not get compassionate leave from prison in England to attend her funeral.
"A week afterwards they were repatriated to Ireland but that grief of not seeing her mother meant she never found closure."
Price's ex-husband and former hunger striker Hugh Feeney, who was also jailed for his part in the Old Bailey bombing, took part in the ceremony.
In later years Price became a vehement citric of Sinn Fein leader Gerry Adams and consistently claimed that he had been her senior commander in the IRA.
She specifically implicated Mr Adams, now a Louth TD, in the kidnap and killing of Catholic mother-of-10 Jean McConville in 1972.
Mr Adams who has always denied being a member of the IRA. He said he had been saddened by Price's death but did not attend today's service.
However, Paul Maskey, Sinn Fein MP for West Belfast, and Stormont Junior Minister Jennifer McCann did go to the Mass.
Afterwards, the coffin - which had been draped in a tricolour - was carried through driving rain half a mile from St Andersonstown to Milltown.
Republicans have a dedicated plot in the cemetery but Price was buried separately.
At the graveside the rain-soaked flag was removed from the coffin, folded and handed to one of Price's two sons.
Family members including her sister Clare and brother Damian then gathered round as the coffin was lowered into the ground and dropped white roses and lillies into the grave.
Veteran republican Bernadette McAliskey was applauded when she told shivering mourners: "We cannot keep pretending that 40 years of cruel war, of loss, of sacrifice, of prison, of inhumanity, has not affected each and every one of us in heart and soul and spirit.
"We cannot keep pretending that the war did not hurt. It broke our hearts and it broke our bodies, it changed our perspectives and it makes every day hard."