The pensioner was found by her son when he arrived to visit her in Townhill Road, Hamilton, on Sunday morning.
Police said she had been unable to get up from the floor or call for help after a man forced his way into her home and attacked her.
The assault happened at about 19:00 on Saturday. The man also stole cash.
The suspect was thought to be in his 50s or 60s and was wearing a dark, hooded top and trousers.
The woman was taken to Hairmyres Hospital in East Kilbride on Sunday where she is in a stable condition.
Officers are checking CCTV and speaking to local residents in the area.
Det Insp David Cockburn said: "Despite the significant inquiries carried out by our officers so far, the man responsible for this horrendous incident has not been caught.
"It is absolutely crucial that we speak to anyone who was in the surrounding area on Saturday evening who may have seen anything suspicious.
"No matter how minor you may think your information is, please let us be the judge of that as it could prove to be vital to our investigation."
A three-figure sum of money was taken from the house.

Investigations are continuing into why the vehicle ploughed into Catherine Bonner's flat in Main Road, Fairlie, at about 13:45 on Thursday.
The A78 through the village is expected to remain closed until early next week.
A 55-year-old man who also lived in the flats continues to be treated for minor injuries at Inverclyde Royal Hospital.
He and the driver were rescued by the emergency services from the rubble. The 54-year-old driver has been released after treatment.
The lorry has been removed from the building and has been taken away to undergo further tests that will help establish the cause of the crash.
North Ayrshire Council said it was working with contractors and engineers to ensure that the properties affected "are made safe".
"Engineers and contractors have started work to secure the affected buildings and it is expected that a partial demolition may be required to ensure the site is made safe," the council said in a statement.
"The council has agreed that contractors can work into and through the night, if necessary.
"It is hoped that this will allow the A78 to re-open early next week."
The council said it had arranged for letters to be delivered to all 600 households in Fairlie informing them of the situation and making them aware that some noise disturbance is likely through the night while work is ongoing.
The statement added: "The council has apologised in advance for any disturbance which may be caused."
Fairlie Community Council has been campaigning for road improvements in the area.
It has argued that the route is not suitable for traffic that includes lorries heading to Hunterston power station.
Councillor John Ferguson, North Ayrshire Council's cabinet member for infrastructure, said: "While responsibility for management of the A78 trunk road lies with Transport Scotland, the council has lobbied - and will continue to lobby - for improvements to the road.
"A draft version of the North Ayrshire Local Plan, published in 2003, called on the (then) Scottish Executive to 'fully assess the need for further improvements on the trunk road network and bring forward schemes at the earliest possible date for the A78 coastal route'.
"While the specific reference to a Fairlie by-pass was removed at the request of the Scottish Executive's reporter, the council's aspiration for improvement schemes along the A78 coastal route remains."

1 August 2016 Last updated at 07:19 BST
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An 86-year-old woman was left on the floor of her South Lanarkshire home overnight after being assaulted in a "horrendous" attack.'
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Work will continue through the night to make safe the site of a house struck by a lorry in an accident that led to the death of a 55-year-old woman.
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