Coach C.K Akunnor's side began the game on a bright note as winger Emmanuel Gyamfi opened the scoring in the 10th minute after capitalising on sluggish defending before easily beating the goalkeeper.
The Porcupine Warriors doubled their lead in the 30th minute courtesy of a solo effort by Maxwell Baakoh. The winger took the ball from the centre of the pitch, ran past three Coton Sports defenders and hit the ball into bottom right corner.
Coton Sport pulled one back before the end of the first half courtesy a penalty converted by their captain Kamilou.
Kotoko began the second half as they did in the first half and were rewarded with the third goal scored by Abdul Fatawu.
Coton again reduced the deficit through Kamilou but Kotoko held on to claim the famous win.
The victory puts the Porcupine Warriors in a good position to reach the knockout stage of the competition for the first time since 2008.
The second leg will take place in Kumasi next week.