Vijay was batting on 76 off 167 balls with the help of 14 boundaries, while Pujara was unbeaten on 55 off 103 balls during which he found the fence seven times at the end of the post-lunch session.
The duo had put on an unbroken 122-run stand for the second wicket as the visitors took hold of proceedings in the Boxing Day Test.
Resuming India's innings at 76 for one in the post-lunch session, Vijay and Pujara further increased their 35-run partnership for the second wicket, playing with consummate ease.
The two batsmen made good use of the conditions, playing watchfully yet at the same time scoring at a decent pace.
India crossed the 100-run mark in the 30th over. The last 10 overs bowled by the Proteas in the post-lunch session had cost 48 runs without producing a wicket.
It was the highlight of the day as run-scoring became easier once the batsmen had got themselves in, something Vijay did with aplomb in the first session as Pujara just carried on his form from the first Test, where he scored 153 in the second innings.
Jacques Kallis (0-23) and Morne Morkel (1-25) bent their backs in the middle phase of the session, trying to get some purchase out of the wicket. But they only had disappointment in store as India raked up 60 runs in the 13 overs bowled in the first hour after lunch.
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