In-form Mario Mandzukic and captain Darijo Srna put the Croatians 2-0 up in the first half before Nikica Jelavic and then a late Mladen Petric goal wrapped up the match, though it was Korea who had the game's first big chance.
Croatia defender Vedran Corluka cleared the ball off the line after a Kim Shin-wook header as both sides wrestled for the initiative.
Bayern Munich's Mandzukic, the Bundesliga's top scorer, converted a perfect cross from Ivan Strinic to put Croatia ahead with a close-range header in the 33rd minute.
Croatia's goalkeeper Stipe Pletikosa, who was celebrating his 100th cap, denied Korea minutes later when he kept out a superb 20-metre shot to keep his side ahead.
Srna guided the ball into the net from the edge of the box four minutes before half-time.
Jelavic had an inspired second half, first putting Croatia 3-0 up after 57 minutes following a defence-splitting pass into the box by midfielder Luka Modric, then providing the assist for Petric five minutes from time.
"After this, we are continuing our qualifying campaign with no headaches. But we are not flying high, we are firmly on the ground and know what is awaiting us," said Croatia's coach Igor Stimac.
Belgium and Croatia share top spot on 10 points in the 2014 World Cup European qualifying Group A while Serbia have four points.
Croatia meet Serbia in Zagreb on March 22 in a match fraught with security risks, as relations between the two have yet to get back to normal following Yugoslavia's break-up and Zagreb's war of independence from 1991-95.
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