Firefighters were called to a blaze in Kilmaurs Road at 23:40 on Saturday.
The woman, local resident Catherine Kelly, was pronounced dead at the scene. A 41-year-old man was taken to hospital with serious injuries. Another woman, aged 41, who was also in the house at the time was not injured.
Police said the fire was a "targeted and deliberate act".
Officers have appealed for witnesses to come forward. They indicated they are following a definite line of inquiry.
Local residents who tried to help put out the blaze were treated at the scene for smoke inhalation.
The injured man was taken to Crosshouse Hospital where medical staff described his condition as stable.
Det Ch Insp Allan Burton said: "The outbreak of fire within the house on Kilmaurs Road has resulted in the death of an elderly woman.
"Following a joint investigation with our colleagues at the Scottish Fire and Rescue Service, we now know that this was a targeted and deliberate act.
"Local residents are understandably shocked and I would like to acknowledge the bravery of those neighbours and passing motorists who raised the alarm and attempted to do what they could to extinguish the blaze.
"I want to reassure local residents that all is being done to trace the person or persons responsible."
Specialist forensic staff and detectives remain at the scene as part of the murder investigation.  Additional uniformed officers are also on patrol in the area.
Det Ch Insp Burton added: "We have spoken with a number of witnesses at this time.
"I would ask any local residents or passing motorists who have yet to come forward and speak to police, please contact us with any information you may have."

The General Medical Council has produced the guidance to make surgical and non-surgical procedures, such as facelifts, breast implants, dermal fillers and Botox, safer.
It will now consult doctors and the public about the guidance.
Plastic surgeons said they were already using a two-week cooling-off period.
In 2013, a report by NHS England's medical director highlighted the risks associated with the cosmetic sector.
This followed safety concerns after nearly 50,000 women in the UK had PIP breast implants fitted. The French implants were made from an unauthorised silicone filler and were found to have double the rupture rate of other implants.
In January, the Royal College of Surgeons published a consultation on proposals to improve standards in cosmetic surgery.
The GMC sets the standards that are expected of all UK doctors who carry out cosmetic procedures. It also tries to help patients understand what to expect from their doctor.
Some of the main points in the new guidance say that doctors should:
Prof Terence Stephenson, the chairman of the General Medical Council, said some patients in this area were vulnerable and needed protecting.
"We are clear that doctors must not pressure patients to make rushed decisions they may end up regretting and they must give them enough information so they can make an informed choice."
Rajiv Grover, consultant plastic surgeon and former President of the British Association of Aesthetic Plastic Surgeons (Baaps), welcomed the GMC's guidance because he said some patients were psychologically unsuitable for cosmetic surgery.
"Cosmetic surgery has for too long been seen as a commodity but unfortunately once an operation is done - it can't be taken back to the shop."
He said Baaps had insisted on a two-week cooling-off period for many years and also encouraged a second consultation with a surgeon before a decision was made.
The association is looking into developing a screening tool to help identify patients who should not have surgery.
The final GMC guidance is expected to be published in early 2016.

The 24-year-old midfielder sustained the injury just 26 days after joining Posh from League Two side Crewe.
He had an operation on Saturday and is expected to be out until November.
"I haven't seen a grown man cry like that for 15 years so I feel for him, but we'll just have to pull together," McCann told BBC Radio Cambridgeshire.
"There were about six seconds left of training, he planted his foot and broke his leg.
"He's had an operation, but I'm sure he'll come back stronger. The lads and the staff are devastated for him."
McCann also confirmed that Posh had not taken up the option to sign trialist striker Morgan Ferrier, who played in the pre-season friendlies against West Ham and Norwich.
A murder investigation is under way after a 71-year-old woman died in a fire at a house in Kilmarnock.
[NEXT_CONCEPT]
Doctors who carry out cosmetic procedures should give patients time to think before agreeing to go ahead, new guidance says.
[NEXT_CONCEPT]
Peterborough United manager Grant McCann has backed Brad Inman to recover from the broken leg he suffered with "six seconds left of training".