South Africa were 126 for no wicket at lunch with Elgar on 72 not out and his opening partner Aiden Markram on 54.
It was a familiar tale for Bangladesh after their captain, Mushfiqur Rahim, won the toss and chose to bowl, as they had done in the first Test in Potchefstroom.
On that occasion Elgar and Markram put on 196 for the first wicket, setting up a 333-run win for South Africa.
As predicted there was more pace and bounce than in Potchefstroom but although there was good carry for the fast bowlers, it also encouraged stroke play from the batsmen.
Fifteen runs came off Roy's second over, the fourth of the match, and Rahim made a double bowling change, with Mustafizur switching ends.
The left-handed Elgar, with a reputation for solid accumulation rather than flashy strokes, hurried to his half- century off 59 balls.
Markram was more subdued at the start of the innings but reached his second fifty in his second Test off 81 balls, with eight fours.
South Africa reached 50 off 77 balls and 100 off 145 deliveries.
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