The four goals all came in the opening half, with Thabiso Kutumela scoring twice to bring his team back from a goal down on two occasions.
The penalty shootout then provided a whole lot of drama before Kwanda Mngonyama buried the decisive kick.
The Team of Choice were off to a disappointing start when they conceded in the 10th minute after goalkeeper Bongani Mpandle was controlled a back-pass but then allowed Mpho Matsi to steal the ball off him before scrambling it into the net.
United gradually fought their way back into the match and had a couple of sniffs at goal, including a 17th minute shot from Kutumela which was deflected for a corner.
The visitors’ efforts paid off in the 22nd minute when Tebogo Tlolane drew a foul from Nyiko Mobbie just inside the box and a penalty was awarded.
Kutumela stepped up confidently and dispatched the spot kick with conviction to level matters up.
However, parity was only to last for a few minutes as Stellenbosch went back in front through Leleto Skelm, who latched onto a loose ball in the box after Maritzburg failed to clear a log throw-in.
The hosts were nearly ahead when Ryan Moon got onto the end of a cross, but from point-blank range Mpandle made a brilliant save to keep out the header.
At the other end, Jeremy Brockie beat the off-side trap and went clean in on goal, but took too long to get his shot away.
The Team of Choice were back on level terms however when after a breath-taking move involving Miguel Timm, Tlolane and Daylon Claasen, who provided the final ball, Kutumela netted a superb effort from a tight angle into the roof of the net.
The second half proved to be a far less frenetic affair, chances few and far between.
The Cape side had a good chance on the hour mark when Moon turned and fired narrowly wide on the half volley.
Maritzburg meanwhile weren’t able to make much in the way of openings although they did come close with 15 minutes to go when Brockie and Phumlani Ntshangase nearly succeeded in stealing the ball off home keeper Boy de Jong.
For the most part though the closing stages of regulation time were cagey with neither team wanting to give anything away.
The game opened up a bit in extra time, although apart from a couple of blocked crosses for Clive Augusto and Kutumela, United failed to open up the Stellenbosch defence.
The hosts meanwhile were close to scoring early on in the second stanza of extra time when Granwald Scott curled an effort inches wide.
To penalties it went and it was looking good for Maritzburg after Siyanda Xulu, Yusuf Jappie, Augusto and Claasen all converted their kicks, while Nathan Sinkala hit the bar and Mpandle got his revenge when he saved Matsi’s effort.
But the drama was to go up a few notches as Kutumela and Timm both hit the post with their spot kicks.
Mngonyama however was to show nerves of steel as he netted his penalty to send United through to the next round.
Stellenbosch: De Jong, Mobbie, Johannes, Ndlovu, Sinkala, Matsi, Mthethwa, Mbekile, Skelem, Karuru, Moon
Subs: Pool, Scott, Isaacs, Mathabela, Gould, Rayners, Bergman
Maritzburg: Mpandle, Mngonyama, Morgan, Xulu, De Reuck, Ntshangase, Timm, Claasen, Tlolane, Kutumela, Brockie
Subs: Barr, Allie, Shandu, Augusto, Jappie, Kunene, Buchanan
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