Emmanuel Clottey scored the winner for the side in the 47th minute in a keenly-contested match.
Tema Youth came into the match on the back on a resounding 3-0 win over Medeama last Sunday and were poised for an upset.
Chelsea have learnt lessons from previous stuttering performances and wanted to build on the 4-1 win at Wassaman.
The win keeps the club in sixth place and three points behind leaders Asante Kotoko