Van Tonder (117, 129b, 10x4, 1x6) and Breetzke (115, 132b, 8x4, 1x6) put paid to the host sides hopes of bouncing back from a 202-run loss to Afghanistan in the quarter-finals as they added 231 runs for the second wicket in 37.3 overs, South Africas highest partnership in the tournament history.
The result of the match between the two losing quarter- finalists gives South Africa a chance to play the winner of Sundays match between Bangladesh and England on January 31, to decide the fifth place.
South Africa, champions in 2014, took control through van Tonder and Breetzke after electing to bat at the Hagley Oval.
The pair batted for a major part of the innings and the team total would have been more than the 284 for six that they managed, had they got a few good cameos down the order.
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New Zealand were bowled out for 211 in reply with Dale Phillips (74, 82b, 5x4, 1x6) fighting it out without much support as South Africas new-ball bowlers wreaked havoc.
Left-armer Akhona Mnyaka finished with two for 49 and had the satisfaction of accounting for a well-set Philips.
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