Torres was recalled to replace Cesc Fabregas up front and scored in the fourth and 70th minutes as Spain outclassed Ireland to win 4-0 in Gdansk, Poland.
However, the defending champion can still be eliminated depending on results in the final group games on Monday.
Elsewhere, UEFA fined Germany for its fans’ uncharacteristic behavior – hurling paper missiles at Portugal players – and a court in Warsaw sent more Poles to prison for violence on the city’s streets on Tuesday.
Spain’s players stamped their authority on Euro 2012 after seeming unsettled in a 1-1 draw with a lively Italian side in their first match.
After Torres lashed in his first goal, the familiar Spanish short-passing style was quickly established and Ireland struggled to see much of the ball.
“With the early goal, everything was easier and the performance of the team was great tonight,” Torres said.
David Silva got a second goal in the 49th, and Fabregas fired a fourth in the 83rd after coming on for Torres.
The final whistle blew on Ireland’s Euro 2012 hopes with its fans singing The Fields of Athenry.