Notoane’s team had won the first leg 5-0 at home last weekend and qualified for the tournament which will be held in Egypt in November.
The three top teams to emerge from the tournament will automatically qualify for the 2020 Olympics. Notoane had warned his team against complacency ahead of the second leg.
“We knew that it was going to be a difficult match going into this second leg,” Notoane said.
“Zimbabwe played with more numbers in their attacking third and we had to manage that. I am also glad with how the boys responded to demands of this game.
“They managed the pressure really well. We are happy with the result and we are also looking forward to our group fixtures going into this year’s U-23 AFCON tournament,” he added.
South Africa now join Zambia, Nigeria, Egypt (hosts), Ghana, Cameroon, Mali and Ivory Coast for the Afcon tournament. The eight teams will be divided into two groups with the top two finishers in each group advancing to the semifinals.