The hosts opened the scoring through Ndzinisa in the opening five minutes as they beat the Stars defensive line, who were caught in no-man's land, before slotting home past a hapless Hoffman.
Two minutes later Ndzinisa added a second as he steered home a header at the near-post from a Swallows corner.
Dikwena had a good chance to pull one back after 15 minutes as Ng'ambi forced the Swallows keeper into a reflex save to deny his powerful header from six yards out.
Shilongo won a penalty in the 20th minute, then stepped up to slot home from 12-yards out to halve the home side's lead.
Stars were fortunate to be handed a second penalty just before half-time, as a Swallows defender's attempted clearance struck his hand, with the referee harshly pointing to the spot, but Abia Nale's poorly placed effort was saved.
Shilongo created two promising opportunities for himself before the hour-mark, but the Swallows goalkeeper was up to the task on both occasions.