Detectives revealed a man - matching the description of the killer - tried to steal a BMW from a man outside the Spar shop in Crookston at around 11.15pm. Around two and a half hours later, police believe the same man broke into the house and killed Isabelle Sanders and attacker her partner Norman Busby. Police are now following a definite line of inquiry and have identified a suspect. Mr Busby, 85, remains in hospital.
Officers say the man they are looking for may have blood on his clothes.
Elite detectives from Police Scotland's Major Investigation Team are working to establish a motive for the killing.
Officers raced to the home the couple had shared for more than 20 years, in a quiet cul-de-sac in Crookston, in the city's south west.
When they arrived at Raeswood Drive, police found Ms Sanders' body and her partner seriously injured.
Mr Busby was rushed to the Southern General Hospital, where he is in a serious condition.
The alarm was raised shortly before 2am yesterday but detectives remained tight-lipped about who called police.
Superintendent Brian McInulty, one of Glasgow's most senior officers, said: "Police were called to a report of a man in a house at around 2am.
"The circumstances of this incident are very unusual.
"This is a very safe community, patrols have been stepped up, and anyone with any concerns should approach officers."
Forensic officers spent hours combing the scene for clues in a bid to find out more about the killing.
A car, which was parked in the driveway, remained covered in blue tarpaulin until it was removed by officers shortly before 3pm.
Superintendent McInulty refused to go into details about how the vehicle was linked to the investigation.
Police issued a description of man reportedly seen at the house. He is a white male, 20 to 30-years-old, around 5ft 10in, of slim build with short dark hair.
He spoke with a local accent and was wearing jeans, a light blue top, and blue canvas deck shoes.
Detective Superintendent Jim Kerr said: "Inquiries are ongoing and specialist officers and forensic teams are currently at the scene.
"Officers are carrying out door to door inquiries and checking CCTV to assist with this investigation.
"I would ask anyone who was in the area, and saw a man matching the description or anyone who recognises the description, to contact police as soon as possible.
"Officers are working to establish a motive for this murder.
"I would like to reassure the local community that additional police patrols are in the area."
Anyone with any information is asked to contact Police Scotland on 101.