The Rockets were hoping to maintain their unbeaten start to the 2020/21 season having drawn 1-1 with Swallows FC in their previous game.
Abafana Bes'thende were also keen to preserve their unbeaten record for this term after drawing 2-2 with Kaizer Chiefs in their last match.
Galaxy dominated the first-half, but they were wasteful with Lindokuhle Mbatha, Karabo Tshepe and Ebrahim Seedat all guilty of missing clear cut chances in the first half.
The Rockets were left to rue their missed chances in the second-half as Abafana Bes'thende broke the deadlock following a mistake by the hosts with 18 minutes left on the clock.
Gerald Modisane attempted a back-heel pass and Pule Mmodi intercepted the ball and fired past Galaxy goalkeeper Websten Van Der Linde to make it 1-0 to Arrows.
However, the Rockets pushed for the equalizing goal in the dying minutes of the match and they managed to score in the last minute.
Mokete Mogaila was the man, who scored to ensure that the encounter ended in a 1-1 draw which left Arrows and Galaxy placed seventh and eighth respectively on the league standings.
Usuthu were keen to bounce back to winning ways after succumbing to a narrow 4-3 defeat to the defending champions Mamelodi Sundowns in their last game.
While the Citizens were looking to record their second successive win after defeating Bloemfontein Celtic 4-2 in their previous match.
The hosts were awarded an early penalty after Taariq Fielies was adjudged to have fouled Lehlohonolo Majoro in the box just three minutes into the encounter.
Former Orlando Pirates marksman Majoro then dusted himself down and clinically converted the penalty-kick to make it 1-0 to AmaZulu.
City then pressed the home side and they did level matters five minutes before half-time when Abbubaker Mobara set-up Prince Agyemang, who netted with a low effort to make it 1-1.
AmaZulu suffered a blow after the restart as Majoro was shown a straight red for a horrific challenge on Thamsanqa Mkhize and the hosts had to play with 10 players.
The home side frustrated the Citizens with some resolute defending and ultimately, the match ended in a 1-1 draw on the night.
The result sees AmaZulu climb up to the ninth spot on the league standings, while City also moved up to sixth place.