Eaves was born in Calgary, spent some years in Blackwood, New Jersey, and grew up in Faribault, Minnesota. He is the son of former Calgary Flames and Minnesota North Stars standout Mike Eaves, formerly the head coach of the University of Wisconsin–Madison's men's hockey team and current head coach of the Columbus Blue Jackets' American Hockey League affiliate Cleveland Monsters, who coached Patrick at the 2004 World Juniors.