Angela Hamilton went into Riggi’s cell at Cornton Vale Prison, Stirling, after breakfast and cut her face with a razor blade.
She left Riggi lying in her cell with her face covered in blood and a clump of her hair missing.
Hamilton then calmly walked back to her cell as prison guards rushed to Riggi’s aid, alerted by her screaming.
Hamilton, 40, denied the attack, but a jury of ten women and five men at Stirling Sheriff Court took just over an hour to find her guilty by majority.
Her lawyer, Murray Aitken, said Hamilton suffered from a variety of problems including drug abuse.
Sheriff William Gilchrist deferred sentence until 3 October for background reports and released Hamilton on bail.
Hamilton made no comment after the verdict.
The attack took place in November 2011 while Hamilton was serving a sentence for attempting to pervert the course of justice.
Riggi was in Cornton Vale during her first year of a 16-year sentence for killing her three young children in Edinburgh, in a crime that shocked the country. The court heard she was regarded as a “high-profile” prisoner.
During the two-day trial, prison officer Calum Graham told how he went to Riggi’s cell that morning after hearing screaming, saw Hamilton leaving the cell and then Riggi lying on the floor inside with blood on her face, still screaming.
His colleague James McCabe said his hands and clothing became “covered in Riggi’s blood” as he tried to help her.
The court was told Riggi, originally from California, had a history of self-harm which was on record in prison, and had been diagnosed with a personality disorder and paranoia.
She tried to kill herself twice in prison a week after being assaulted by Hamilton.
She had previously tried to kill herself after stabbing each of her children – eight-year-old twins Austin and Gianluca, and their sister Cecilia, five – eight times at their home in the Scottish capital in 2010. She leapt from the second-floor flat after trying to cover up their deaths with a gas explosion.
Riggi was originally charged with murder but admitted culpable homicide on the grounds of diminished responsibility.
She was later transferred to a secure mental hospital in England and was found dead in her cell there in March this year.
A coroner ruled that the 50-year-old died from natural causes at Rampton Secure Hospital in Nottinghamshire.
Pathologist Dr Geoffrey Hulman, concluded that she died from bronchial pneumonia.
Hamilton was jailed for six years in 2009 when her brother walked free from a murder charge after she failed to give evidence at his trial.
Daniel Hamilton was acquitted of murdering Paul White, 22, at a flat in Pollokshaws, Glasgow, in 2004. Her father Joseph was found guilty of the murder and jailed for 17 years.