Russia started positively but were hit on the counter-attack, with Fernando Torres squaring for Villa to roll home.
Konstantin Zyryanov saw a shot hit the post but then Villa prodded past Igor Akinfeyev to double the lead and after 74 minutes he drilled in a third.
Roman Pavlyuchenko nodded a consolation before Cesc Fabregas headed a fourth.
"When I think of Villa, it's a name that makes me think of scoring," said Spain coach Luis Aragones after the Group D opener.
"Villa is a brilliant player but so is Torres when he's got space."
Valencia forward Villa hit back at doubters of the camaraderie in the Spanish camp after the game as he also paid tribute to Torres.
"There's a lot of talk from outside about whether or not the squad is united," he said.
"I don't agree with all this talk."
He added: "I wanted to dedicate that third one to him because I owed him something for the first two.
"He made the first one and his run opened up the space for (Andres) Iniesta to make a pass."