The 77-year-old victim answered his door to the two men, who assaulted him and then stole money and personal belongings from his Bothwell home.
Detectives are now appealing for anyone with information about the "cowardly crime", which took place at approximately 10.45pm in Wingfield Gardens and left the pensioner shaken but without serious injuries.
The first suspect was wearing a green tracksuit on the night of the attack and is described as approximately 5ft 7in tall, and of slim build.
The second suspect is also thought to be about 35 years old and about 5ft 7in, but was wearing a white tracksuit
Detective sergeant Laura Sands, from Cambuslang police station, said: "For someone to force their way into this elderly gentleman's home and subject him to such a terrifying ordeal is absolutely despicable.
"It is crucial that we trace the people responsible for this cowardly crime as soon as possible and officers are currently examining CCTV and speaking with local residents as part of their enquiries.
"I would urge anyone who was in the local area on Saturday evening to come forward if they think they may have seen the two men responsible, or anything suspicious.
"I would also be keen to hear about any vehicles seen in the area of Wingfield Gardens around the time of the robbery.
"Local residents will understandably be concerned following this incident and there will be additional police patrols in the area to provide reassurance. If you have any concerns at all, please feel free to speak to the officers who will be happy to assist you."
Anyone with information is asked to call 101, quoting incident number 3976 of 28 December 2019.
Alternatively, possible witnesses can contact Crimestoppers on 0800 555 111, where details can be given anonymously.