The Lions of the North were not at their best on the night but did enough to collect maximum points against the Chilli Boys.
Given Msimango profited from a mistake made by the United defence when he pounced on a free ball in the box to open the scoring.
Striker Tendai Ndoro beat veteran Patrick Tignyemb from a long way out to extend Highlands leads and secure three points.
Chippa United looked disjointed when they went forward in an attempt to trouble the Lion of the North seeing most of their forward moves cut shot.
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