Jones, playing only his second match of the tournament, grabbed five for 33 while left-arm bowler Mnyaka took three for 27 as Bangladesh were bowled out for 178 in 41.4 overs.
The 2014 champions, put in to bat in the fifth-sixth position play-off match, quickly reached 180 for two in 38.3 overs as captain Raynard van Tonder played a fluent knock of 82 (99b, 7x4, 2x6) to tally his total runs to 384 in the tournament.
"We did not play well in the quarter-finals, but the boys did well to come back strongly in the last two games," Van Tonder said.
Bangladesh captain Saif Hassan said his team should have got more runs in the match today: "These have been good conditions for us and they have given us good exposure. We don't get these conditions at home so hopefully this experience will help us in the future."
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Van Tonder reached his half-century with a pulled six over the square-leg fence off leg-spinner Mohammad Rakib and continued in the same vein, adding 117 runs for the unbroken third wicket with all-rounder Hermann Rolfes (44 not out, 51b, 7x4) to eradicate any hopes of a Bangladesh fight back.
Bangladesh were reduced to 33 for five in the ninth over and in danger of being dismissed for a two-digit score before left-hander Afif Hossain (63, 59b, 7x4, 2x6) and Shakil Hossain (61, 89b, 6x4) did the repair-work with a 96-run stand in 18.9 overs.