Akimi Barada also scored for the visitors in an exciting clash as Kashiwa recovered from an early Yeom Ki-hun goal while Jong Tae-se pulling a goal back for the home side midway in the second half.
In the second minute Suwon got off to a great start when Seo Jung-jin found Jong on the left side and sent in a cross where Yeom was on hand from six-yards out to poke home past goalkeeper Takanori Sugeno.
Ten minutes later Kashiwa equalised when Cristiano put through a curling pass for Barada to hammer a low shot past goalkeeper Jung Sung-ryong to make the score 1-1.
Kashiwa took the lead in the 28th minute when Sang-min was adjudged to have fouled Kosuke Taketomi in the area when both went up for a header. Leandro stepped up and beat Jung with the penalty.
The visitors increased their lead 10-minutes after the restart as Cristiano broke down the right to send in a low cross for Leandro to sweep home and make the score 3-1.
Suwon pulled a goal back in the 59th minute as Yeom was given space on the left and curled a cross onto the head of Jong, who made no mistake from close-range.
In the last 30-muntes Suwon dominated through attacking but Kashiwa held firm to keep their slender advantage.
The second leg takes place at Hitachi Kashiwa Stadium on May 26.