Her mother Louise Baillie, 38, and father Adam Shaw, 35, asked mourners attending Dalrymple Parish Church, East Ayrshire, to pay tribute to the girl by wearing her favourite colour.
Every pew in the church overflowed with family, neighbours, school friends and teachers who turned out yesterday to pay their respects
Her favourite Christmas hymn, Away in a Manger, was played just before the service began with a white coffin dressed with pink flowers and a photograph placed at the altar.
The Reverend Lawrie Lennox said: "You may be surprised to hear Away in a Manger playing at this time of year, but it was one of Rachel's favourites and you would hear her singing it at any time of year."
Rachel died in hospital on Saturday night after contracting a deadly strain of E. coli in July following a trip to the United States, where her father lives
She was initially treated in Crosshouse Hospital, Kilmarnock, and allowed home when her condition seemingly improved but shortly afterwards her blood count plummeted and she was transferred to Yorkhill Hospital.
Rev Lennox said: "We should be confident that Rachel has now gone straight from her loving family on earth to God's family in Heaven. I can see her now exploring the place and making lots of new friends."
She said Rachel's family were finding comfort in reflecting on how much the little girl packed into her short life.
He said: "She would have been nine in October and she experienced more in her eight years than some would in 80 years."
An ardent singer, reader and writer, Rachel spent her early life living in South Wales before moving to East Ayrshire.
She spoke both English and Welsh and enjoyed holidays in America where she visited dad Adam who worked in Texas.
Rev Lennox said Rachel's teachers in Primary Three and Four at Dalrymple Primary School described her as a "light" whose unwavering love of school often put her teachers to shame.
After the first hymn – Make Me a Channel of Your Peace – was sung, Rev Lennox said if the congregation took away the song's message into their own lives "Rachel's life will not have been lived in vain".
Another song chosen for the funeral, One More Step Along the World I Go, was another favourite of Rachel's school.
As Rachel's family and mourners, many in tears, made their way out of the church, Katy Perry's Firework was played.
Donations were made by mourners to the Yorkhill Hospital for Sick Children