Small said two of the girls reacted by smashing one of her front windows as they left.
The victim called a neighbour who placed a couch up against the window to secure it overnight.
The woman went to bed but was woken by a smoke alarm and the couch engulfed by fire.
Luckily, she was not injured and firefighters put out the blaze.
Small said it was an "absolutely appalling" crime and police were following positive lines of inquiry. "An innocent elderly victim was targeted in her own home, a place where she should have been able to be safe and feel safe."
He said the elderly could call for help if they were in situations where they felt unsafe.
"Often our elderly community feel like they may be wasting police time or being a bother by ringing us, but we are here for them when they need us and we encourage them not to hesitate to call us," said Small.
"We know the Ranui community will be as horrified as we are by this and so we urge anyone with information to call police as soon as possible."
Age Concern Auckland chief executive Kevin Lamb said older Aucklanders were often targeted.
"It is an unfortunate reminder for us all to regularly check on our neighbours, friends and family, and to call the emergency services without hesitation."
Anyone with information was asked to contact Waitakere Police Station (09) 839 0600 or Crimestoppers anonymously on 0800 555 111.
