The couple's two surviving children Michael, six, and Tom, four, have been left orphaned.
Fr Derek Farrell, parish priest to the Travelling community, said the young brothers were reunited after Tom was released from hospital earlier this week "thanks to the outstanding courage and bravery of his young uncle John".
John, 15, risked his own life to save others in the horrific fire at a halting site on the Glenamuck Road, and was "a hero and a source of immense pride," the priest told mourners.
There were heart-wrenching scenes at the funeral Mass at the Church of the Ascension of the Lord in Balally, Co Dublin, where grief-stricken family members had to be physically supported by others.
Mourners were led by Thomas' parents, Jim and Jojo, as well as his and Sylvia's brothers and sisters.
Children queued up outside to take turns reaching into the fleet of hearses to touch the small white coffins of their three cousins and blow them a final kiss.
Sylvia's brother John Lynch sobbed as he recalled during the ceremony spending the day before the blaze with them and waking the next day to find out all his family were gone.
"I said good night to them, we had a lovely day.
"They left that night, and when I woke up the next morning I did not believe it.
"I thought it was a hoax, the moment I realised all my family was gone, my brothers and my sister, my brother in law , my sister in law and my nephews and nieces."
On Tuesday, his brothers Jimmy, 39, Willie, 25, Willie's pregnant partner Tara Gilbert, 27, and their daughters Jodie, nine, and Kelsey, four, were buried.
Inconsolable, he was applauded by the congregation as he thanked the "people of Ireland" for their support.
Fr Farrell told mourners the epicentre of a tragedy that visited the Lynch and Connors home on October 10 had sent shock waves through the land.
"Thomas and Sylvia, as a couple, were seen as a match made in Heaven," he said.
"Deeply loving and devoted to each other, they never left each other's side.
"They never seemed to fall out or have any serious argument. They were very close as man and woman, husband and wife."
Married for nearly eight years, they were "the best father and mother that any children could ask for," he told the funeral.
"Thomas loved his family, his family was his life," he said.
"Sylvia, in the words of her mother-in-law Jojo, was 'the best girl you could ask for'.
"She loved being a mother herself, and was a very good mother. Her husband and her children were her life."
Young Jim loved to stay with his grandparents and was a very happy boy, while Christy was full of life, "Daddy and Mammy's little boy", mourners heard.
"They were both very clever for their age, and both were waiting on the birth of their baby sister," said Fr Farrell.
"When Baby Mary came she was much treasured by the whole family."
Fr Farrell praised a widespread instinctive outpouring of support for the families, describing it as a "watershed moment" in relations between Travellers and the settled community.
"As a lasting meaningful tribute to those devastated in this tragedy we must build on the immediate gestures of generosity and sympathy," he said.
The priest also reiterated remarks by Fr Dermot Lane, a local parish priest, who said the tragedy had rightly disturbed the consciences of everybody and raised serious questions about accommodation for the Traveller community.
Several survivors of the blaze, including children, were left without somewhere to stay in the aftermath.
Residents in a south Dublin cul-de-sac objected to their being temporarily sited in an adjacent publicly-owned field.
President Michael D Higgins was represented at the funeral by his aide de camp Col Michael Kiernan, while Taoiseach Enda Kenny was represented by Commandant Kieran Carey.
Communications Minister Alex White, Sinn Fein leader Gerry Adams and deputy leader Mary Lou McDonald as well as local Independent TD Shane Ross also attended.
Bishop Ray Field, auxiliary Bishop of Dublin, represented Archbishop Diarmuid Martin.
A message from Pope Francis read out at Tuesday's funeral, expressing his deep sadness at the tragedy, was read out again.
Bishop Field said representatives of the Travelling community in Ireland will travel to Rome tomorrow to personally meet the Pontiff "and hear his own words of sympathy".
After the funeral Mass, the bodies of the Connors family were taken to the Church of the Assumption, Bride Street in Wexford, where they are to be buried tomorrow at Crosstown cemetery.
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