The 70-year-old man died after the house was partially buried in a "sea of mud" unleashed after the hill behind the building gave way as a result of the unprecedented volumes of rainfall experienced across swaths of northern Italy in the last two weeks.
Rescue workers managed to drag the 16-year-old granddaughter from the rubble after more than four hours of digging but she died later in hospital.
A neighbour described how he had been awoken during the night by a huge bang "like fireworks".
"Then my house began to shake. Firefighters and civil protection officers were there very quickly and started digging with spades, even with their bare hands. The parents were helping them ... It was a horrific scene," the neighbour told Italian television.
The tragedy means a total of 11 people have died in accidents related to the freak weather conditions in just over a month.
Genoa is particularly vulnerable to flooding because the foothills of the Alps climb steeply from immediately around the city. The city experienced 139 millimetres (five and a half inches) of rain in a matter of hours on Saturday. The Liguria region has had as much rain in the first 15 days of November as it normally gets in an entire year.
There will also be legal repercussions.
Three landslide deaths last week are already the subject of manslaughter investigations and in Genoa there is anger among residents that the city was not better prepared after floods in 2011 that left seven dead.
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