The West Asians represented a much more difficult test for the Taeguk Warriors who had recorded a comfortable 6-0 victory over Lebanon in their opening qualifier
The Taeguk Warriors had routed Lebanon 6-0 on Friday, with Park netting a hat-trick in the victory, but Kuwait represented a sterner challenge.
Hosts Kuwait started brightly, with midfielder Waleed Ali unleashing a vicious fourth-minute strike from range which stung the palms of Korea keeper Jung Sung-Ryong.
However, four minutes later Korea were ahead when a fine passing move was finished off emphatically by new Arsenal signing Park after Ji Dong-Won's clever feign from Nam Tae-Hee's threaded pass on the edge of the box.
Kuwait responded with intent after the goal with local hero Bader Al-Mutwa firing in an effort from a difficult angle on 10 minutes, forcing Jung into a save.
The Suwon Bluewings keeper was called into action again on 22 minutes after his poor throw was swooped upon by Ali who flashed in a cross-cum-shot which had Jung scrambling but he parried the ball away.
As the half wore on, the Taeguk Warriors looked for a second although they lost full-back Cha Du-Ri due to injury which didn't help their cause in defence.
On 39 minutes, Nam drove forward and shot narrowly wide from outside the box, while Kuwait's Yousef Nasser had a long-range low drive saved moments later.
However, Kuwait's breakthrough came eight minutes into the second-half when they raced forward before Hussain Fadhel scrambled the ball home from close range.
The home crowd got behind Kuwait as they searched for a winner, while Korea offered the odd threat, but it ended 1-1.