The service took place at St Agnes' Catholic Church in Andersonstown on Monday morning.
Irish actor Stephen Rea, who was married to Price between 1983 and 2000, carried the coffin during the procession.
Price, 62, was found dead at her home in north Dublin last Wednesday night.
Gardai said they did not suspect foul play.
She was convicted, along with her sister Marian, for their part in the IRA car bomb attack on London's Old Bailey courts in 1973 in which one man died and more than 200 people were injured.
She spent eight years in jail including several weeks on hunger strike before being released in 1980.
Her funeral was not attended by Sinn Féin President Gerry Adams.
The pair clashed over her allegations that he had been a commanding officer in the IRA, something Mr Adams has always denied.
Price had claimed that Adams, former West Belfast MLA, had been involved in the kidnap and killing of Jean McConville in 1972, one of the so-called 'disappeared'.
Mr Adams expressed sadness at the news of her death last week.
"I have known Dolours for a very long time," he said.
"She endured great hardship during her time in prison in the 1970s enduring a hunger strike which included force feeding for over 200 days.
"I want to extend my sincere condolences to her family and especially to her two sons, Danny and Oscar, and her sister Marian."
Price made the claims in an interview with American university academics known as the Boston College tapes.
PSNI launched a legal battle to acquire the tapes, which were recorded in the understanding that they would not be published until after Ms Price's death.
But they will not automatically handed over to police, historian Anthony McIntyre, who was involved in the interviews, indicated.
Her sister Marian Price, also known by her married name McGlinchey, has been imprisoned since 2011 after her licence was revoked by the then NI Secretary of State Owen Paterson for dissident republican activity.
The 58-year-old was released for a few hours to go to the wake on Sunday following an emergency judicial review at the weekend.
She was later returned to a secure unit at Belfast City Hospital where she is being held due to her ill health.
Her lawyer, Kevin Winters, claimed it was highly significant that the Prison Service will now foot the legal bill for the judicial review.
"It's a case that should never have had to see the light of day in court," he said.
"It's a matter of regret that we had to go to court to enforce her right to grieve with her family."
The burial took place at Milltown Cemetery following the service.