Pirates progressed to the quarter-finals but they were in trouble in the first stanza after Thabiso Kutumela got an early goal for United against his former side.
A tactical change at half-time won the game for the Buccaneers, as Kabelo Dlamini, who came on for Ben Motshwari, found the equaliser 11 minutes from the break, with Deon Hotto making it 2-1 a minute later and Vincent Pule killed the game in the last 12 minutes with the third goal.
"It's not so easy, Maritzburg is not a bad team, in the past time they made a very good game but they have a little bit unluck at the moment to score, we know this," Zinnbauer told SuperSport TV after the match.
"You see we made a mistake in defence, we were not so in the game, they made the space very tight, this was the reason in the first-half we were not so in the game, a lot of good attacks.
"We came to the last third but the solution, the decision [making] was not right. At half-time we spoke about this in the dressing room and we changed a little bit the system and it comes better in the game.
"You see Dlamini comes in, he scored, Pule makes the next step. We have then this, what we expect from Pirates, take the control of the game, lead the game and win the game, that's the point we had to do. We knew before it was tough but I think deserved."