Marcel Kaheza scored a penalty for Polisi Tanzania to deny the hosts a clean sheet.
Azam s victory came just after they condemned Premier League rivals Yanga SC 1-0 a few days ago. The Ice-cream Makers have made the stride into the next knockout phase looking to win a trophy they last lifted in the 2018/19 season.
Meanwhile, Biashara United defeated Ruvu Shooting 4-1 in the other game. After a 1-1 draw at full-time, Biashara United went on to pick the win from the spot-kicks to book their place in the round of the last eight.
Simba won the cup last season and since they had lifted the league, the Caf Confederation Cup slot - which is guaranteed to the winner of the local competition - was given to Namungo FC by virtue of being finalists.