South Africa went into the match against their neighbours as clear favourites, having won all of their previous matches in the competition and already secured their place in the knockout round.
Zimbabwe, on the other hand, had lost both of their Super 8 matches with no way to fight their way into the semi-finals but nevertheless raised their game and made the Proteas work for their win.
Sikandar Raza won the toss and chose to bat on a decent wicket but they did not get off to the best start with Tadiwanashe Marumani being bowled by Kwena Maphaka in just the second over.
Zimbabwe struggled to build momentum early in their innings as wickets fell at regular intervals.
However, Raza stepped up with a real captain's knock of 73 off 43 balls with eight fours and four sixes to help his side post a defendable total.
Clive Madande chipped in with a valuable 26 off 20 balls down the order as Zimbabwe reached 153/7 from their 20 overs.
Maphaka was the pick of South Africa's bowlers with figures of 21/2 off his four overs. Corbin Bosch also picked up a couple of wickets, while George Linde, Lungi Ngidi and Anrich Nortje got one each.
The Proteas' response got off to a rocky start, with Raza backing himself with the opening over and picking up the crucial wicket of Quinton de Kock.
Raza continued to shine as he bowled Aiden Markram in his second over to keep South Africa under pressure.
Ryan Rickelton and Dewald Brevis were able to steady the innings with scores of 31 and 42, respectively.
Brevis runs came off just 18 balls, which helped put the Proteas in a strong position heading into the business end of the match.
David Miller (22), Tristan Stubbs (21*) and George Linde (30*) all got runs as South Africa reached their target with five wickets and 13 balls to spare.
They advance to the semi-finals at the top of Group 1 and undefeated throughout the entire tournament so far.
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