Advocate depute Alex Prentice, QC, told the jury at the High Court in Edinburgh that the 38-year-old was murdered by David Gilroy in the basement of the building where they both worked on May 4, 2010.
During his closing speech, Mr Prentice said it was an "unusual" case as there was "no evidence of a dead body".
Gilroy, 49, from the Silverknowes area of the city, denies murdering Ms Pilley in Thistle Street, Edinburgh, or elsewhere in Scotland, by unknown means on May 4, 2010.
He also pleads not guilty to a charge of attempting to defeat the ends of justice between May 4 and May 6, 2010, by concealing Ms Pilley's body and transporting it to various locations in Scotland in the boot of a car.
Earlier, defence QC Jack Davidson told jurors Gilroy had decided not to give evidence in the trial.
The court heard from witnesses called by the defence who worked in the same office building as Gilroy and Ms Pilley, and said they had not noticed anything out of the ordinary on the day she disappeared.
A police officer who had searched Gilroy's car days later said he had not noticed any smell in the boot.
The prosecution's closing speech began with Mr Prentice telling jurors how Ms Pilley had been seen making her "routine journey" to work on the morning of May 4, 2010.
He said: "The Crown case is that Suzanne Pilley met David Gilroy on that morning; that they went to the basement in the building together, quite possibly with the consent of both; that he killed her, he placed her body in the recess, he got his car from home, brought it to the garage, placed her dead body in the boot, took her home and next day transported her to a lonely grave somewhere in Argyll where she is now."
Mr Prentice said he had to establish to the jury Suzanne Pilley is dead and said they should reject the idea she could have committed suicide.
He said she had not made any arrangements for her cat Mercury to be cared for and she had not withdrawn money from her bank account nor used her credit cards.
Mr Prentice said: "I suggest there is absolutely no basis for thinking she is somewhere else, alive, hiding from family and friends."
Voicemails left on her phone on May 1, 2010, were played in court. Mr Prentice said they were from Gilroy, asking her to get in touch and that he was "a wee bit worried".
Mr Prentice said the calls, voicemails and text messages stopped the day before she went missing and Gilroy did not text after that day.
He added there was "nothing from him, nothing at all". He said: "I suggest the most glaringly obvious reason for that is he knows there is no purpose in doing that because she is dead and he has her phone."
Mr Prentice claimed all the "different strands" made up the "cable of evidence". He told the jury that taking all these strands together "creates a compelling and convincing case of murder committed by David Gilroy".
He added: "I suggest there really is only one just and appropriate verdict in this case. I would ask you to return a verdict of guilty to both of the charges."
Trial judge Lord Bracadale told jurors Mr Davidson would give his defence speech today.