The woman was attacked after the man entered through an unlocked window at the apartment in Hulme, Manchester, at about 5am on Tuesday, Greater Manchester Police said.
Det Supt David Meeney said the man was being sought by officers in connection with the rape and a subsequent robbery.
Urging people to be “vigilant”, he said such attacks were “very rare”.
Appealing for information, he added that the attack was being treated as an isolated incident, but locals should “make sure their doors and windows are secure, especially during the late evening and through the night”.
The force said extra patrols would also be deployed in the area.
