Omony turned a cross by Lebogang Mokoena into his own net on the stroke of half-time.
Although the Buccaneers dominated for most parts of the first half, they almost fell behind in the second minute of the game when Bucs’ keeper Senzo Meyiwa was forced into a tipping a Darrel Smith header over the bar.
Gilbert Mushangazhike then sent his header wide from a Teko Modise free-kick, as Pirates imposed themselves on the game.
The visitors were awarded a free-kick on the edge of Celtic’s area in the 37th minute, but Modise saw his effort tipped around the post for a corner, which was taken by Modise and culminated in Lucas Thwala’s shot being cleared off the line by Cyril Mubiala.
Pirates went ahead seconds before the break when Mokoena’s cross from the right was turned into his own by Omony.
The score remained 1-0 at the break.
Pirates continued their dominance in the opening stages of the second half and Omony almost produced another blunder when he allowed Tlou Segolela’s shot to spill between his legs, but the Celtic stopper was able to gather the ball just before it crossed his goalline.
Both sides then rang the changes, which spoilt Pirates’ momentum, allowing Celtic to get back in the game.
The host should have drawn level in the 79th minute when an unmarked Mubiala sent headed over the crossbar from Grant Smit’s free-kick.
The final chance of the game also fell to Celtic in the final minute of the game when they were awarded a free-kick on the edge of the Pirates area, but Smith sent his effort high over the bar, and with that went Phunya Sele Sele’s hopes of securing at least a point from the game.