A Geofrey Massa bullet handed the hosts the lead on the half-hour mark as the Ugandan opened his account for Phunya Sele Sele.
Celtic enjoyed the majority of the ball and created the better chances going forward in the first half, with Massa and strike partner Lerato Lamola causing a headache for the under-pressure Cosmos defence.
An early Massa free-kick from the edge of the area evaded the entire Cosmos defensive line as Sherwyn Naicker was called on early for the save, before a Keagan Buchanan set-piece was headed clear.
Musa Nyatama tried his luck from range after showing good strength to win the ball in midfield, yet his shot failed to find its target.
Celtic’s pressure finally paid off as goalkeeper Patrick Tignyemb cleared the ball long which Massa controlled expertly with his chest before unleashing an unstoppable shot to put Celtic in front.
Cosmos had the perfect opportunity to level matters just eight minutes later as Wandisile Letlabika handled in the box to hand the visitors a penalty, yet Tignyemb saved Charlton Mashumba’s strike to preserve his side’s lead heading into the break.
Early second half action saw Wiseman Maluleke unleash a ferocious long-range strike which Tignyemb tipped over the bar, while on the other end of the pitch, Lamola was unlucky to find the right-hand upright after squeezing his shot away from just inside the box.
Celtic refused to sit on their lead as the continued to press forward while nullifying the Cosmos attack, who could not break the stubborn Siwelele defense.
Try as they might, Cosmos could not find the leveller as Celtic won their third consecutive League encounter, lifting them to fourth in the Premiership standings, while Cosmos remain second-bottom in 15th.