Kirsty Nelis, 36, from Inverkip, was on board the police helicopter which plunged through the roof of the Glasgow pub, killing nine people.
Family, friends and Police Scotland staff gathered for a Requiem Mass at St Andrew's Cathedral, just 200m from the scene of the tragedy.
The married officer was part of the police's helicopter unit and had received a commendation for her bravery in the past.
Ten uniformed officers lined the entrance to the cathedral and saluted as the coffin, bearing a police hat, was carried in to the sound of a lone piper.
PC Nelis's family, including husband Mark, also a police officer, lead mourners.
Chief Constable of Police Scotland, Sir Steve House, First Minister Alex Salmond and Justice Secretary Kenny MacAskill attended the service led by the Archbishop of Glasgow Philip Tartaglia.
Glasgow Lord Provost Sadie Docherty and council leader Gordon Matheson were also present.
The crash occurred when Pc Nelis and colleague Pc Tony Collins, 43, were
returning from an
operation on Friday
They were killed alongside pilot David Traill, 51, and six others inside the pub. The funeral of fellow officer Tony Collins was held on the Isle of Arran yesterday.
Archbishop Tartaglia today offered his "deepest sympathies" to the family as he welcomed mourners.
Mourners sang How Great Thou Art as the coffin made its way to the front of the cathedral.
Mr House and a police colleague delivered readings during the hour-long service.
Clutha owner Alan Crossan and bar manager
Saverio Petri, who was using crutches, attended the mass
A message from PC Nelis's family on the mass booklet thanked the public and relatives for their "profound kindness" .
Archbishop Tartaglia said: "We offer our deepest sympathies to Kirsty's husband Mark, to her mum and dad, to her two brothers, and to all her relatives and friends.
"We know that you have been devastated by Kirsty's tragic, sudden and untimely loss.
"Together with you, putting our hope in Jesus, we pray for her eternal rest."
The cathedral, which holds around 1000 people, appeared to be full, with many mourners listening while standing in the doorway.
During his sermon the Archbishop said: "Mark and Kirsty's family are rightly proud of her, but their hearts nonetheless ache for the loss of her. And that pain will not go away quickly.
"My dear friends, you must comfort one another and allow yourselves to be comforted. You will be comforted by your love for Kirsty and her love for you, by your pride in her, by many wonderful memories; and all of these
precious and personal things will help to sustain you through this difficult and trying time."
The service was
followed by a private family burial at Clydebank Crematorium.
The funerals of two other men who were in the pub, Mark O'Prey, 44, and Gary Arthur, 48, were held on Monday, while the funeral of the helicopter's pilot, Captain David Traill, 51, was held at Glasgow University on Saturday.
Three other pub customers - Robert Jenkins, 61, Colin Gibson, 33, and Samuel McGhee, 56, - also died.