Thapelo Matlhoko got Usuthu underway with his goal on 22 minutes before Sekhukhune levelled with four first-half minutes remaining.
Nkosikhona Radebe restored AmaZulu's lead five minutes into the second half but substitute Bright Ndlovu ensured a share of the spoils with his goal after 76 minutes.
The result left Zwane's side in fourth place on the league standings with 38 points from 23 games, and Babina Noko in fifth place with 35 points.
Speaking after the game, Zwane called on his team to retain their belief ahead of their match with Siwelele at the weekend.
"When you look at all the goals and look at all the turnovers, we gave them the ball," said Zwane in the Citizen.
"You could see now when they started showing respect, they wanted to manage the game. And they wanted to attack in moments rather than playing a game.
"They knew that they would open up, so they wanted to manage us, especially towards the end of the game.
"They were just playing for that point. You will find that situation when you play with players who are still growing. We just have to be patient and have belief."
