The survivors were an elderly couple and an 8-year-old boy, police Sgt. Travis Welsh said.
No one else had been reported missing.
All three were taken to a hospital. Their conditions weren't immediately known, but Welsh said the man was talking to rescuers.
"It's pretty incredible that we pulled three living bodies out of there," Welsh said.
Part of the house was upended and lying on its side, and the area around it appeared to be strewn with debris. A utility pole tilted at a pronounced angle.
The elderly couple lived in the house that was destroyed. Police weren't sure if the boy lived there or elsewhere.
The avalanche slid down Mount Jumbo into the northeast Missoula neighborhood at about 4 p.m.
Authorities say avalanche conditions around the city remained dangerous Friday night after a storm brought blizzard conditions to much of the region.
Police asked residents of vulnerable neighborhoods to consider leaving but did not require or recommend evacuations, Welsh said.
Neighbors and the first responders to reach the scene dug frantically through the snow and debris, the Missoulian reported (http://tinyurl.com/mb6nf6p).
Firefighters with avalanche probes long poles used to penetrate the snow to find victims then took over, and the boy was pulled from the snow at about 5:15 p.m.
The Missoulian reported the man was found about an hour later and his wife about an hour after that.
A natural gas leak was also reported in the area, and utility crews were summoned.
Cheryl McMillan, who lives near the house that was destroyed, told the Missoulian she heard a roar, but didn't know what it was at first.
"Then, when we looked again, we saw that their whole house was kind of no longer there, at least the top floor," she said.
McMillan said she has lived in the neighborhood for 31 years and has never seen an avalanche before.