Amakhosi, however, are through to the next round with a 5-2 aggregate‚ having beaten Zimamoto 4-0 in the first leg in Port Elizabeth last week.
Yussuf Mtuba converted two penalties for the home side‚ while Lebo Manyama scored the consolation goal for Chiefs in the second half.
Chiefs will have to wait until Wednesday night to know their next round opponents will be between Madagascan side Elgeco Plus and Unidad Malabo from Equatorial Guinea.
Elgeco currently lead the tie 3-1 on aggregate.
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