Navas goal gives Spain victory
The European champions fielded mainly second-choice players and were restricted to few sights of goal until the closing stages when the substitutes made their presence felt.
Arsenal midfielder Fabregas, linked with a move to Barcelona this week, played for an hour without any problems.
"It's been a tough match. We are coming off a long season and a build-up with a lot of training sessions, morning and afternoon, and it tells," Fabregas told Spanish state television.
"The first half was better than the second for me. This has all been a bit like a pre-season for me, but I am feeling good."
Striker Fernando Torres remains the only Spanish player not to have featured in the warm-up matches as he continues his recovery from knee surgery.
South Korea produced a well-organised display in their last warm-up game before travelling to South Africa, where they begin their Group B campaign against Greece on June 12.
Fabregas, starting his first match since cracking a bone in his right leg in Arsenal's Champions League quarter-final first leg against Barcelona two months ago, had the clearest chance to open the scoring after 35 minutes.
Juan Mata carved the opening and Fabregas curled a shot against the crossbar, but despite their overwhelming possession Spain struggled to break down their opponents.
The Koreans looked sharp on the counter and Pepe Reina made a double save from Park Chu-young and Lee Chung-yong after a well-worked move just before the break.
Barcelona goalkeeper Victor Valdes won his first Spain cap in the second half as both sides rang the changes.
Spain substitute David Villa made a few good chances before Sevilla winger Navas picked up the ball outside the area and fired a spectacular shot into the top corner four minutes from time.
After a sluggish 3-2 win over Saudi Arabia last weekend Spain continued to look a little slow and predictable.
They have one more friendly against Poland next Tuesday before starting out in Group H against Switzerland on June 16.