Two goals in the first half from Ruzaigh Gamildien and Thokozani Mshengu secured victory for the visitors while the consolation goal, scored by Alton Meiring, was not enough to salvage a result for Ezenkosi.
It was a first half dominated by the away team and they played some free-flowing football.
Cosmos' best chance of the game came in the opening minute of the match when Bamuzo Sono fired inches wide from 12 yards out – under no pressure.
Following that early scare, Celtic found their footing in the game and started taking control of the possession stakes, while Cosmos looked shaky in defence and were only able to stop the visitors attack by conceding free-kicks.
In the ninth minute Gamildien struck a well-placed free-kick from the edge of the box round the defensive wall and into the top corner of the net to make it 1-0.
Celtic continued to dominate, but seemed unable to find the right pass in the final third.
Gamildien created the second goal through some great individual work which allowed Kgotso Moleko to find some space down the right flank where he supplied an accurate pass to Mshengu 12 yards out from goal.
Meshengu grabbed the opportunity with both hands and superbly slotted the ball into the bottom right corner of the net to double his side’s lead.
Cosmos came out renewed side in the second half, and came close in the 50th minute when Siyabonga Nhlapo tried his luck from 20 yards out, but his effort was well saved by Thabani Stemmer.
But three minutes later there was nothing Stemmer could do to stop Meiring's clinical finish from 12 yards out to pull a goal back for Cosmos.
That was as bright as the night got for the home side as they could not find the equaliser, and stay rooted to the foot of the table after their 12th defeat of the season.