But yesterday they discovered their mistaken belief had cost them a total of 15 and a half years in jail.
Judge Lady Wise told the trio: "This was a carefully planned attack."
She added: "The manner in which it was carried out was callous and brutal."
Patrycja Brzozowska was found in her Motherwell flat by Avon cosmetics representative Chiree Klepp who was on her rounds in the 17-storey tower block.
Ms Klepp, 22, told how she heard muffled cries for help but all she could see through the glass in the door of the flat was a head swathed in black and yellow tape.
She called the tower-block's caretaker, Kenny Watson, 51, who ignored Ms Brzozowska's protests and called police.
Ms Brzozowska had managed to free her feet and get to her door, the trial heard.
Her wrists were tied so tightly with cable ties that her hands were white and the tape round her mouth almost prevented her from speaking.
Ms Brzozowska, 27, had answered her door in Merryton Tower thinking she was about to welcome a punter.
At the High Court in Edinburgh, Jason Barton, 41, of Pentland Court, Coatbridge, was sentenced to six years in prison.
John Coulter, 24, of Douglas View, also Coatbridge, was jailed for five years because he has less serious criminal record.
David Coulter, 21, of Craigavon, County Armagh, Northern Ireland, was given a four and a half year sentence because Lady Wise said he was "effectively a first offender."
All had been found guilty of assault and robbery.