"(Considering) how much possession of the ball we had ... we were caught out by our own mistakes," said Russia coach Guus Hiddink, whose successful streak at major tournaments is in danger of coming to an end. "I hope we can move fast now because we still have two games to go."
Villa showed no effects from the right thigh injury picked up a week ago as he took his international goal tally to 17 from 32 games, two more than Torres, who has played 50 times.
"When I think of Villa, it's a name that makes me think of scoring," Spain coach Luis Aragones said. "The Spanish team has the luck of having players that can score. It could be Villa today or Torres tomorrow."
But without left back Joan Capdevila, the first two goals would not have been possible.
The Villarreal defender found Torres down the left with space. In a one-on-one situation with defender Denis Kolodin, the Liverpool striker worked around the Dynamo Moscow defender to feed Villa for a calmly struck goal.
Capdevila led the breakout on the second goal, too, finding Iniesta with a cross-field pass. Iniesta left Yuri Zhirkov flat-footed as the agile FC Barcelona player moved around him to feed Villa, who had slipped between two defenders and alone in front of Akinfeev for another crisp finish with his right foot.
Villa paid tribute to Torres after scoring the third goal with another impressive individual move, running over to the bench to hug his teammate, who had come off for Fabregas in the 54th.
Spain's David Silva (L) is tackled during the Euro 2008 Group D football match between Spain and Russia at Tivoli Neu Stadium in Innsbruck, Austria, June 10, 2008. Spain won 4-1. (Xinhua/Yuan Man)
"He had a very important game and he is a key player to us so I wanted to dedicate that third one to him," Villa said of Torres, who scored 33 goals in 47 games in all competitions for Liverpool last season.
Russia faces defending champion Greece and Sweden to avoid dropping out after the group stage for the fourth straight time. Hiddink has never failed to lead his teams out of the group phase at four prior major championships.