Chippa actually took the lead at the Moses Mabhida Stadium through Azola Matrose after 34 minutes.
But it was all Usuthu from then on in as Athini Maqokola first levelled after 43 minutes and Sphamandla Zikhali put the home side into the lead for the first time on the stroke of half-time.
The Chilli Boys were improved after the break, but Zwane's side raised their game and scored three more unanswered goals (Maqokola 73', Thapelo Matlhoko 78', Thabiso Kutumela 90') for a convincing win.
The result left AmaZulu in fourth place on the Betway Premiership standings with 42 points from 26 games, four adrift of Kaizer Chiefs in third, although from two games more.
Chippa are down in 13th place with 24 points from 26 games.
Speaking after the game, a delighted Zwane lauded his team as well as young Maqokola for his brace.
"We needed that energy when setting defensive traps and the right attacking energy from our nine, and I think the choice we made was correct. Because we knew Chippa's energy would die after 30 minutes," Zwane said in the Citizen.
"Our players executed the plan very well. Even after we conceded the first goal, I wasn't panicking at all. I knew we were going to come back.
"My only worry was whether or not we took our chances. And this is one of those games where we created a lot of chances. I'd say more than enough to win by at least seven or eight goals. So, I think we were not clinical.
"But if there's a player I'm happy for, it's Athini (Maqokola). He has been the main culprit for us for the last five games."
Usuthu next play Golden Arrows at the Moses Mabhida Stadium on Wednesday 6 May.
Their remaining fixtures for the season include Orbit College, Kaizer Chiefs and Durban City.