Ross Wright, 19, attacked the 25-year-old woman at a house in Clydebank, West Dunbartonshire, on 24 May.
He claimed the woman was awake and had consented to have sex but was convicted following a trial last month.
Wright was on early release from detention for a serious assault charge when he carried out the rape.
Jailing him at the High Court in Edinburgh, temporary judge Kenneth Maciver told Wright: "You took sexual advantage of a woman who you knew from prior observation to be fully asleep through the effects of a alcohol.
"It is clear to me that from the evidence that was placed before the court that you waited for your opportunity to enter her room before sexually assaulting her.
"You have been convicted of a despicable crime and I have to make it clear to you that an extended sentence is appropriate."
The judge ordered Wright to be supervised for 21 months following his release from jail. The 19-year-old was also placed on the sex offenders' register.
Wright's trial heard how the woman and friends had been at an 18th birthday party which was also attended by Wright.
At the end of the evening the woman went to sleep in a bedroom of the house and was woken up by Wright having sex with her.
A teenager who raped a sleeping woman months after being released early from prison has been jailed for six years and three months.