The Proteas were briefly in trouble at 36-2 after winning the toss but rallied strongly, taking 144 runs off the last 10 overs to finish on 382-5 amid a barrage of boundaries.
It was a total Bangladesh never looked like chasing down as they collapsed to 58-5.
That they were eventually dismissed for 233 was largely due to Mahmudullah’s run-a-ball 111.
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But by the time the 37-year-old veteran completed just his fourth one-day international century in 195 innings, the match had long since ceased to be a contest, with no other Bangladesh batsman making more than 22.
South Africa have now won four of their opening five World Cup matches, with the only blot a shock loss to the Netherlands.
