Barry Hunter, 22, and Arran Adey, 26, had spied on Eilidh Carr from the garden of her Edinburgh home before the midnight break-in, the High Court in Edinburgh heard.
They told her she was a silly lassie who should lock her windows.
Adey was caught because he cut his finger stealing coins from a jar and a bloodstain matched his DNA.
Ms Carr, 20, was threatened with a screwdriver as the men ordered: "Don't move." One of them said they had been watching the flat and had seen her through her window, said advocate depute Martin Macari. "She described herself as being 'totally frozen' at this point."
At the end of her hour-long ordeal she was made to sit on a chair and was trussed up with tape. As the men left they locked the door behind them. Ms Carr was able to get free but when she tried to call for help she found the phone wire had been cut. She climbed through a window and ran to a neighbour.
Hunter and Adey, both of Edinburgh, admitted the break-in on August 7 and assaulting and robbing Ms Carr in her Piershill home.
They also admitted using her bank card to withdraw £80 from a cash machine.
Lord Turnbull called for background reports and remanded both men in custody, pending sentence in Glasgow next month.