Alexander was convicted of assaulting David Hoggan to his severe injury and permanent disfigurement by hitting him on the head with a glass and stabbing him on the body with a knife.
He was originally charged with attempted murder but a jury at the High Court in Livingston convicted him of the reduced charge.
Co-accused Thompson was convicted of attempting to murder Bryan Simons by stabbing him on the body with a knife.
The attacks took place at a flat in Dalry Road, Edinburgh, on May 25 last year.
During the trial the court heard that Alexander smashed a pint tumbler over Mr Hoggan’s head and stabbed him in the left arm and the left thigh. Thompson slashed Mr Hoggan’s girlfriend Kirsty Ogg on the leg and repeatedly stabbed his friend Bryan Simons, puncturing his lung.
Mr Hoggan, 31, of Haymarket, said he needed staples in two head wounds and stitches in the stab wounds.
Mr Simons said of Thompson’s attack: “It was a frenzy. She just came jabbing at me.”
Outside the High Court Mr Simons, who admitted to being scared stiff in the witness box, said the sentences were too lenient. He commented: “Five years is not long enough for attempted murder – I was on the operating table twice after the attack.”
Jailing them, Lady Stacey told both accused they had been convicted of serious offences.
She said she was treating Thompson, who only has one conviction for a road traffic matter, as a first offender. Lady Stacey told Thompson: “Violence is out of character for you.”
Solicitor advocate Jim Wallace, representing Alexander said: “This was sparked by the theft of a purse and money from Miss Thompson.”
Solicitor advocate Maurice Smyth representing Thompson said: “She is in a partnership with Mr Alexander. Sadly she miscarried their baby and also suffers health problems.
“At the time she was on drugs and has little or no recollection of what happened.”
Following the verdict Detective Chief Inspector Sara Buchanan welcomed the result.
DCI Buchanan said: “The injuries all three victims sustained were not only extremely painful, but incredibly serious.
“The sentence handed down to both Wayne Alexander and Nikita Thomson is testament to the proactive approach taken by Lothian and Borders Police and the Crown Office to tackle violent crime.
“We will continue to work to remove those who chose to act violently from our communities.”