The Asian side looked to have turned the game around when Bolton midfielder Lee Chung-yong cancelled out Suarez's early strike with 68 minutes gone. But amid a wintry downpour at the Nelson Mandela Bay Stadium, the Ajax striker curled home a brilliant winner 10 minutes from time to confirm Oscar Tabarez's side as the first team to reach the last eight.
Uruguay were the better side before the break and deserved their half-time lead, but they had to survive a major fightback as Korea refused to give up on their dream, and Uruguay keeper Fernando Muslera had to make a vital late save from substitute Lee Dong-gook to ensure the tie did not go to extra-time.
Had Park Cho-young's fifth-minute free-kick come off the inside, rather than the outside of the post with Muslera helpless, the ball might have ended up in the back of the net and Korea would have been in front. But it did not, and three minutes later with South Korea keeper Jung Sung-ryong fatally reconsidering his decision to come for Diego Forlan's teasing low cross when it was too late to do so, Suarez expertly steered the ball into the gaping net from a tight angle to double the dose for the Asian side.
South Korea returned from the half-time break knowing their World Cup was drawing to a close unless they could find a way back into the game, and they resumed with some intent. Kim Jae-sung only just failed to connect with full-back Lee Young-pyo's cross after it had been dummied by Park Chu-young, and the striker himself blasted over with 51 minutes gone when he might have done better.
The equaliser came with 68 minutes gone after substitute Mauricio Victorino could only half-clear a free-kick and Lee Chung-yong headed home the loose ball with Muslera and defender Diego Lugano flat-footed.
Uruguay's response was swift and Jung had to turn away Suarez's 73rd-minute shot, and it was he who won the game with 10 minutes remaining when, after a Forlan corner had been headed out, he picked up possession on the left and curled home a superb shot off the inside of the upright.