A six-year-old boy and another man who live in the property above were also taken to hospital but have since been discharged.
Police and emergency services were called to the ground floor flat in George Street in the Renfrewshire town just before 9pm on Monday.
There was no one in the flat at the time, but three residents from the block were taken to the Royal Alexandra Hospital for treatment for smoke inhalation.
Only the 51-year-old neighbour from a ground floor flat remains in intensive care in hospital. Staff describe his condition as critical.
A number of other residents were evacuated as a precaution but have been allowed to return to their homes.
Police are treating the incident as wilful fire-raising and appealed for information.
Detective Inspector David Wagstaff said: “Officers, including a forensic team, are carrying out a search of the flat and also speaking to neighbours in an effort to trace the person responsible for the fire.
“Whilst there may have been no-one in the flat that was targeted, this irresponsible and thoughtless act has resulted in a neighbour being seriously ill in hospital.
“George Street is residential and it is entirely possible that people would have been in the street or driving by at the time of the incident.
“I would appeal to anyone who may have seen someone running from the flat or anyone acting suspiciously in the area between 8:45pm and 9pm to contact police.”
Any information can be passed to police via 101, quoting incident number 3687/18/12/17, or by calling Crimestoppers on 0800 555 111.
Police are also investigating a fire in Helensburgh, Argyll and Bute, which led to the evacuation of a mother, her two children and two guests, and completely destroyed a home and business.
Officers believe it may have been started deliberately but are carrying out an investigation to establish the circumstances.
Emergency services were called to the scene on Lomond Street at around 1:25am on Tuesday.
No-one was injured.
Detective Constable David Hardie said: “This fire has completely destroyed a home and business - leaving a family without a home or any belongings.
“It is vital that we find out the exact cause of the fire. With it only being a week before Christmas, the family are absolutely devastated.
“The incident took place in a central area of Helensburgh and therefore there may have been people who were in the area or were woken around the time of the incident.
“If anybody has any information or saw anything they believe to have been suspicious, no matter how insignificant, come forward and contact us.”
Helensburgh police office can be contacted via 101, quoting incident number 0167 of Tuesday, 19 December.