The opening quarter of the match saw both sides failing to find their rhythm and as a result they failed to trouble the goalkeepers.
However, it was the home side who came close to opening the scoring in the 22nd minute when Kagiso Senamela sprung the offside trap to collect a ball played over the defence.
The attacking midfielder then lobbed the ball over the advancing Pavels Steinbors, but could only watch in agony as the ball bounced in front of the line and then came back off the crossbar.
Senamela then continued to cause problems for the Arrows defence and six minutes later he was put through by a brilliant pass from Kulegani Madondo, but he wasted a great chance as he shot wide from close range.
The hosts had another chance to take the lead before the break in the 33th minute but Ayanda Dlamini saw his shot deflected wide for a corner by Musa Bilankulu.
Then after the break Muhsin Ertugral's men came close to breaking the deadlock against the run of play when Ntlantla Zothwane met a cross from Mzivukile Tom with a powerful volley, but his effort flashed wide of the post.
AmaZulu continued to keep more possession but failed to make it count in the final third before Senamela forced a good save from Arrows goalkeeper Pavels Steinbors in the 76th minute with an effort from range.
Two minutes later left-back Marc Van Heerden spotted the goalkeeper off his line and attempted a lob from just over the halfway line, but the goalkeeper recovered well to tip the ball over the crossbar.
The result was good enough to see both sides ending their two-match losing streak, but leaves both teams in the bottom half of the table as they remain winless in the new campaign.