Lee Chung-yong pounced on a mistake by keeper Fernando Muslera with a close-range header just after the hour to cancel out Suarez's early opener in near monsoon conditions in Port Elizabeth.
But the Ajax star wasn't to be denied, and made the most of more lax defending to curl home a stunning winner from the edge of the area with 10 minutes left after Korea Republic failed to deal with a Diego Forlan corner.
The resurgent South Americans will face Ghana or the USA in Johannesburg on July 2nd after deservedly earning a place in the last eight for the first time in 40 years.
After his winner in the final group game against Mexico, Suarez is finally starting to fulfil his billing as an outsider for the competition's Golden Boot thanks to an impressive 49-goal haul for the Dutch club last season.
The Koreans, previously the lowest-ranked country remaining in this their seventh straight appearance in the finals, had enjoyed the upper-hand in the opening skirmishes but were caught napping at the back as Uruguay took an eighth-minute lead.
There was little danger as Forlan, given time and space by Cha Du-ri, sent over a no more than hopeful cross from the left, which should have been easily cleared by a well-manned Korea rearguard.
But with four defenders stood admiring the centre and goalkeeper Jung Sung-ryong rooted almost to his line, Suarez stole in unmarked at the far post ahead of Lee Young-pyo to open the scoring from a narrow angle.
There should have been an opportunity for Uruguay to double their advantage just before half-time when Ki Sung-yueng escaped with what appeared to be a clear handball as he moved to block Maxi Pereira's surge into the area.
Park Chu-young went closest for Korea before the interval, the dangerous forward seeing a curling 25-yard free-kick kept out only by the woodwork, before a powerful left-footed effort from outside the area drifted narrowly wide.
On a poor surface as the pitch cut-up badly right from the start, Cha Du-ri was also unlucky not to make up for his part in Uruguay's goal when a spectacular long-range effort dipped just over with keeper Muslera struggling to make his ground.
Uruguay were almost made to pay for sitting back on their lead as the Koreans stormed back into the contest thanks to Bolton midfielder Lee's brave header midway through the second-half.
Even after Suarez had doubled his and his country's tally near the end, only a desperate late save from Muslera, who atoned for his earlier howler with a great block to deny substitute Lee Dong-gook, prevented the contest from going into extra-time.
Uruguay (4-4-2): Muslera; Lugano, Godin (Victorino 46), Fucile, M Pereira; Perez, Arevalo, Cavani, A Pereira (Lodeiro 75); Suarez (A Fernandez 84), Forlan.
Subs (not used): Castillo, Silva, Caceres, Gargano, Arevalo, Gonzalez, Cavani, Abreu, S Fernandez.
Korea Republic (4-4-1-1): Jung Sung-ryong; Cha Du-ri, Lee Young-pyo, Cho Yong-hyung, Lee Jung-soo; Kim Jung-woo, Ki Sung-yueng (Yeom Ki-hun 85), Kim Jae-sung (Lee Dong-gook 61), Park Ji-sung; Lee Chung-yong; Park Chu-young.
Subs (not used): Lee Woon-jae, Kim Young-kwang, Oh Beom-seok, Kim Hyung-il, Kim Dong-jin, Kang Min-soo, Kim Nam-il, Kim Bo Kyung, Ahn Jung-hwan, Lee Seung-yeoul.