Scott Johnston, 19, admitted forcing his victim to the ground, pinning her down, repeatedly striking her with an iron and raping her before he was put behind bars for six years and nine months.
He claimed he was so drunk he had no memory of the event, but he was snared by CCTV and DNA evidence.
The woman's face was badly bruised and her hair was matted with blood following the attack at her home in Mount Florida on December 8, 2013 .
Judge Lady Rae told Johnston: "All rapes are horrid crimes but what aggravates this is that the complainer was unknown to you, a complete stranger. You entered her home uninvited and forced yourself on her.
"This was a degrading sexual assault and you violently assaulted her with a weapon causing her severe injury."
Lady Rae added: "What is concerning is the level of brutality you are capable of when intoxicated.
"What you did to this lady has had a devastating effect on her.
"She can no longer live in her home."
Defence counsel Gordon Jackson QC said: "My client's position has always been that he was in a state of intoxication and has no recollection of this incident.
"This was a normal decent young man form a decent family until this happened.
"He is a first offender and it is difficult to understand he did what he did.
"There is no explanation in his history. But, he put his hands up and has accepted responsibility for what happened."
Johnston, a first offender, came across the woman outside Hampden Stadium, where he had been at a Christmas party.
He then followed her to her flat where he raped her.