"He said that the main door was locked so he went to the back door which was slightly open," a police spokesperson said.
"He found her lying on the floor in the sitting room and there was blood everywhere."
The Foreign Office confirmed that a British national was killed in Goa on Friday and said that local police were investigating the case as a murder.
The weapon used in the killing, a kitchen knife, was reportedly discovered embedded in Ms Higgins' neck.
Police held 27-year-old Anand Kamble in connection with the killing. He was visiting Ms Higgins, a retired civil servant and widow, at the time of her death.
Mr Kamble's wife and daughter were also visiting and were believed to be in the house sleeping at the time of the murder. They have subsequently disappeared and their whereabouts remain unknown.
Ms Higgins, who moved to India last year, has two adult children.
A sexual motive has been ruled out by police, who said a motive for the killing has yet to emerge.
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