Second-half strikes from Leonardo Castro and Hendrick Ekstein secured the win for the Glamour Boys and Middendorp hailed the character his side showed to bounce back from Saturday's defeat to Sundowns.
"We haven't been disappointed with our performances (of late)," Middendorp told Supersport TV. "We played a very good game against Sundowns. We were just not on our game for crucial moments as everyone knows.
"And then it's always a little bit difficult three or four days later to go with the right, brave attitude in to a game like Bidvest. They are the top team in the PSL. We have seen they are very structured, very clear purpose in their game and yes, you have to counter it.
"I think we have done it in a proper way. We scored two goals. They scored nothing and yes, I'm very happy with the result."
Meanwhile, Middendorp explained the change of mind he had in deciding to take Khama Billiat off instead of Leonardo Castro for Bernard Parker.
"It was a plan to take Leonardo Castro out and put Bernard in but then in this moment he scored.
"And as I always say changing a player doesn't mean he is not performing. But sometimes you need a fresh approach. Then we changed Billiat out for Parker instead, and I think it worked because Leo was very good in the final minutes."