Barcelona played in the Copa del Rey on Friday so their players were rested, though they are likely to play in the friendly against China on Sunday.
Torres had a great chance in the fifth minute when he attempted to divert Cazorla's shot into the bottom left-hand corner, but his instinctive volley whistled just wide.
The Chelsea striker was not to be denied for long and he opened the scoring with a lovely finish six minutes later. Mata crossed from the left, and the 28-year-old backheaded the ball over South Korea’s debutant goalkeeper Kim Jin-Hyun.
But Spain kept up the pressure, with Mata exchanging passes with Torres on the edge of the box, then the 24-year-old midfielder tried to find Silva with a threaded pass, but Kim Jin-Hyun was alert to the danger and quick to come out of his goal to grab the ball.
Spain really should have had a second on 41 minutes, when Silva found Torres with a lovely threaded pass, but the Chelsea striker then passed to an offside Mata rather than take the chance himself.
And Choi Kang-hee’s men took advantage of Spain’s profligacy a minute later, when the ball dropped to Kim Do-Heon on the edge of the box, and the 29-year-old slammed the ball right-footed into the top corner past Reina.
But South Korea gave away two goals in a matter of minutes after the break from a couple of handballs.
In the 51st minute, Cho Yong-Hyung turned his back from a Raul Albiol shot on the edge of the area, but left his hand dangling, and the referee awarded a penalty and a yellow card.
Xavi Alonso made no mistake from the penalty spot for his 13th goal in his 95th appearance, with a penalty low to the keeper's right.
Four minutes later, it was 3-1 after Albiol’s snapshot was this time handled by South Korea goalscorer Kim Do-Heon, and Cazorla’s low free-kick right on the edge of the area went though the wall and into the bottom corner of the goal.
South Korea had a great chance to get back into the game on 69 minutes when Kim Do-Heon slipped the ball through to Kim Bo-Kyung along the line of the penalty area, but the 22-year-old flicked the ball wide of Reina’s goal.
Negredo made it 4-1 in the 80th minute with a low finish underneath the goalkeeper Kim Jin-Hyun for his sixth goal in nine appearances.
The Sevilla forward’s goal was made by Valencia striker Roberto Soldado, who was left out of the 23-man selection for the Euros despite his fine league form and his hat-trick against Venezuela in the friendly in March.
It was a good outing for Spain, who open their Euro 2012 campaign against Italy on June 10, before facing Ireland four days later and then Croatia on June 18.