The 30-year-old Shakhtar Donetsk mainstay curled in a 41st minute strike to add to Mario Mandzukic's earlier header, with Nikica Jelavic coming off the bench to score the third and Mladen Petric adding the fourth at his home ground.
The game started in an open fashion with both sides looking to play attacking football.
Ivica Olic should have opened the scoring after seven minutes but he headed Niko Kranjcar's cross wide despite being free inside the area.
Three minutes later and South Korea came close to taking the lead as Lee Chung-yong's deep cross was headed goalwards by Ki Sung-yueng but Vedran Corluka was able to clear from off his own goal-line.
Olic had another glorious opportunity when Shin Hyung-min gifted possession to Mandzukic inside the South Korea area and the Bayern Munich forward laid the ball into the path of Olic, whose shot was deflected wide.
Mandzukic took matters into his own hands and put Croatia ahead as he headed home Ivan Rakitic's free-kick after 33 minutes.
Stipe Pletikosa, also collecting his 100th cap in goal for Croatia, then tipped Ji Dong-won's shot over the bar before his captain Srna doubled Croatia's lead four minutes before half-time with a great solo effort from the edge of the box.
Croatia killed off the game in the 57th minute when half-time substitute Jelavic latched on to Luka Modric's through ball to tuck away his first chance of the game.
Lee Dong-Gook almost pulled a goal back for South Korea as he latched on to a tame defensive header by Corluka but his effort fizzed just wide of Pletikosa's left-hand post.
A raft of substitutions throughout the second-half took the sting out of the game with Petric adding a touch of class to proceedings as he chipped Jung Sung-ryong for Croatia's fourth with five minutes remaining.