Anthony Russell, 39, has previously admitted the murders of Julie Williams, her son David Williams and 31-year-old Nicole McGregor, whose body was found in woodland near Leamington Spa.
The jury heard he had assaulted Ms McGregor just hours after she showed him a picture of her baby scan.
Russell is due to be sentenced at Warwick Crown Court on Friday.
Police described him as an “evil” and extremely dangerous individual and said the “violent series of killings” had taken place over “a period of just seven days” in October 2020.
West Midlands Police said it believed Mr Williams was killed due to Russell’s “mistaken belief that he was in a relationship with his girlfriend”.
When Russell then went to speak to Julie Williams about her son’s disappearance, Det Supt Shaun Edwards said he suspected “he confessed to David’s killing” and he “then killed Julie to stop her from speaking to the police”.
There was “no known link” between the killer and Ms McGregor, he added.
After a retrial, Russell was unanimously found guilty of rape.
He had pleaded guilty to the murders of Mrs Williams, 58, and Mr Williams, 32, at separate flats in Coventry on 25 October and 21 October 2020 respectively.
He had also admitted the 26 October murder of Ms McGregor, who was found three days later.