They had been gassed by a car accidentally left running in an internal garage, police believe.
The television was still playing for Cindy George's daughter Pio (5) and two sons, Teuruaa (3) and Telyzshaun aged 2.
Ms George - who was admired for her strength as a single mother - was found just metres from her children in a hallway.
Born in the Cook Islands, Ms George moved to Ashburton about five years ago to work and was separated from their father, who also lives and works in Ashburton.
Mid-South Canterbury area commander, Inspector Dave Gaskin, said it was a very unusual death but an accidental tragedy.
The grief and shock of devastated family and friends as they crossed the red and white police emergency tape on Thomson St in the suburb of Tinwald was shared throughout the small township today.
"You can feel it when you come into Ashburton," said Bishop Moea Pongia, of the Latter Day Saints church where Ms George and her children were devout members.
"You can feel the community and know something has gone on here, you can feel it."
The "awesome family" are known widely in the Mormon and Cook Island communities, where they are considered family despite Ms George's relatives living mainly in her native Rarotonga.
The house they were sitting was an "immaculate" townhouse, rented by perfect tenants known as friendly, chatty neighbours.
A line of police officers in uniform removed their hats and bowed their heads as hearses drove past in procession today. Family members accompanied by an officer left the property showing obvious signs of distress.
Police will remain in place at the house overnight until a full scene examination can be completed tomorrow morning. A team of 30 staff are working on the investigation.
Tributes on social media
There have been tributes on social media from family and friends - many who were hearing the news of the deaths via social media messages.
"God please comfort my family for our loss. Fly high my aunty and three little cousins," Ms George's niece Eireene Atingakua wrote on Facebook.
She posted a photo of the family and was letting relatives and friends know the details of their deaths.
"Rest in loving peace my beautiful aunty Cindy George and our baby cousins. Unbelievable and shocking that yous (sic) have left us too early."
Alana Kavana said: "Rest In Peace Cindy and your adorable children. Definitely taken away too early but you are in the Lords arms now... Condolences to the family."
Ms George's friend Christine Isamaela said she was "so shocked" to hear the disturbing news.
"Not sure wat really happened they found Cindy & her kids dead... probably from some sort of gas leak," she wrote on Facebook. "Just watching the news makes me cry."
Community upset
Ashburton people are "upset" their small town has made the news for the second time in a year following the tragic discovery yesterday afternoon.
This morning, Ashburton Mayor Angus McKay said although residents would carry on with their lives today, they were sad to see their community once again clouded in tragedy.
"No one in a close net community likes a tragedy such as this. They are upset that Ashburton is on the news for such a tragic event."
It is almost a year since the town was left reeling when two Work and Income staff were shot dead. Russell John Tully, 48, has been charged in relation to the incident on September 1.
Today, Mr McKay said the community would "absolutely" band together, "as it always does" to offer their support. Thoughts were now with the family, friends and neighbours of the deceased, he said.
- NZ Herald and Ashburton Guardian