Odey, who joined FC Zurich from Nigeria Professional Football League (NPFL) side MFM FC last season, was an unused substitute in the game.
Despite having a player sent off in the second half, FC Zurich still held on for the win.
FC Zurich took the lead in the 11th minute thanks to Michael Frey but were reduced to 10 men following Sangone Sarr’s sending off on 67 minute after receiving his second yellow card.
Antonio Marchesano made it 2-0 to FC Zurich in the with 16 minutes left despite playing with 10 men.
In the 80th minute, Young Boys pulled a goal back through Miralem Sulejmani which ended up being a consolation goal.
FC Zurich have now won the Swiss Cup 10 times after last winning it in 2016.