The incident – thought to have been a targeted attack – took place at a property in Wide Lane, Morley, shortly after 9.20am yesterday.
Two men arrived at the address wearing high-visibility jackets and claiming to be police officers with news about a relative.
As they came into the property, however, the 54-year-old female occupier noticed one of them was carrying a screwdriver and duct tape.
She attempted to flee but the men grabbed her and threatened her with a knife.
The woman was left tied to a radiator in her bathroom as the pair made off with a “substantial” amount of jewellery and cash.
A picture of a car and an e-fit of one of the robbers were today issued by police.
The suspects are described as white and in their 20s. One had particularly pale skin and blue eyes.
Leeds District CID’s Det Insp Mark Swift said: “This is a serious offence in which a woman has been threatened with a knife and restrained in her own home, leaving her fortunately uninjured but understandably also deeply upset.
“I am appealing for information from anyone who may recognise the man pictured, saw two men outside the property wearing high-visibility jackets or who saw the suspect vehicle shortly after the incident.”
He added: “This was an unusual incident for the Morley area and we believe this was a targeted rather than random attack.
“I want to reassure residents a number of active inquiries are under way.”
Anyone with information is asked to ring Leeds District CID on 0113 241 4642 or Crimestoppers anonymously on 0800 555111.