The point leaves AmaZulu eighth, but Cosmos remain bottom on 17 points with three games remaining.
Jomo Sono's men could conceivably catch either Santos or Black Leopards, if they win their final matches and the other results go in their favour.
Cosmos had two half-chances early on, when Alois Ngwerume hit a tame shot wide, and Katlego Loke almost scored from a corner-kick, which Tapuwa Kapini had to acrobatically flick wide.
Dumisani Zwane missed the best chance for AmaZulu when his shot was saved by Avril Phali.
The visitors' best chance of the second half came when substitute Siyabonga Nontshinga fired just over the crossbar after a Cosmos counter-attack.
Meanwhile AmaZulu's best shot at the win came from Ayanda Dlamini, who was played in on the left. The striker shot from a tight angle, but it was straight at Avril Phali.
It was a game of much goalmouth action, but no converted chances, and AmaZulu may come to regret the draw when it comes to the top eight at the end of the season.