Amla and Elgar added 119 runs off 304 balls for the second wicket on a pitch that appears to have become less threatening.
Just four overs before tea, Ishant Sharma dismissed Amla, while Bumrah accounted for AB de Villiers to give India a glimmer of hope.
At the break, Elgar was batting on 61 runs, while Faf du Plessis (0*) was giving him company in the middle with South Africa still needing 105 runs with 7 wickets in hand.
The duo batted calmly and took South Africa past the 100 -mark.
Ishant (1-27) bowled a tight spell after lunch, but India struggled to string together a bowling partnership that could put Elgar-Amla under pressure.
Soon the duo raised a 100-run stand, the first in this Test, and Elgar reached his 10th Test half-century off 153 balls.
At the other end, Amla crossed 50 off 134 balls, his 38th in Test cricket. It was also the 9th time that he scored twin half-centuries in the same Test.
The long-awaited wicket finally came in the 53rd over when Amla chipped Ishant straight to midwicket and was out caught by a diving Pandya, much in the same manner as the first innings.
India made it a double blow as three overs later, AB de Villiers (6) was caught at gully off Jasprit Bumrah (1-46) to give themselves a glimmer of hope.
The umpires Aleem Dar and Ian Gould had two inspections at 10 am and 10.30 am (local time). After the second inspection, they were happy enough to allow play to resume 30 minutes later.
Finally the game began at 11 am local time, with all three sessions rescheduled, after an hours delay. The morning session was 90 minutes long.
Elgar encountered a couple hairy moments once again, against Bumrah in particular, but settled down shortly enough. He shrugged off whatever happened last evening and looked more confident as the session went on.
At the other end, Amla looked ever solid. He left the ball well and looked to score whenever the opportunity presented itself.
India gave away too many quick runs early on in the session, not helped by uneven bounce as they conceded 9 extras in the first hour of play. But later they tightened up the scoring.
Kumar and Ishant Sharma (0-10) managed to keep things quiet though, even as Amla and Elgar built their gritty partnership.
South Africa crossed 50 in the 22nd over, while their 50 -partnership came off 125 balls. They made good use of heavy roller in the morning, which might have sedated the pitch somewhat.
To their discredit, India didn't even create a single half-chance for getting a breakthrough this morning.
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