Pujara and Vijay showed great levels of patience and kept the South African pacers at bay as India took a 145-run lead. Virat Kohli was the other unbeaten batsman on six.
Vijay was unlucky to be dismissed, poking at a delivery outside the leg-stump and getting a faint edge.
South African bowlers once again adopted their negative approach of bowling well outside the off-stump and the Indian batsman were more than happy to leave them alone.
But the biggest set-back that South Africa suffered in the day was when pacer Morne Morkel left the field with a right ankle sprain early in India's second innings.
Earlier in the day, inspired performances by pacers Zaheer Khan and Ishant Sharma helped India take a first innings lead of 36 runs after bowling out South Africa for 244.
At lunch India, reached 31/1, increasing the lead to 67 runs.
Shikhar Dhawan (15) was the only Indian wicket to fall in the morning session as he became Vernon Philander's 100th Test victim, caught at second slip by Jacques Kallis.
Ishant Sharma (4/79) registered his best figures on South African soil and Zaheer Khan (4/88) made a sensational return to international cricket after 12 months as South Africa suffered their second batting collapse. Mohammad Shami got two for 48.
South Africa, who lost five wickets for 16 runs on the second day, lost another flurry of wickets on the third day in their first innings as, resuming at 213/6, they lost the last four wickets for 31 runs. Overnight batsmen Vernon Philander made 59 and Faf du Plesis made 20.
Philander's knock was ended by Zaheer who pitched it outside the off-stump, short of length, and the edge flew to Ravichandran Ashwin at first slip.
Dale Steyn (10) smacked two consecutive fours off Zaheer but was removed by Ishant, who ducked it short as the South African tried to fend it away but only managed to edge it to Rohit Sharma in the slips.
Zaheer struck again in the next over to dismiss Du Plesis, caught behind by Mahendra Singh Dhoni and then went on to wrap up the innings with a yorker to castle Morne Morkel.
India 280 all out and 109/2 (Vijay 39, Pujara 39 batting, Kohli 6 batting; Philander 1-31, Kallis 1-23) vs South Africa 244 all out (Smith 68, Philander 59; Zaheer Khan 4-88, Ishant Sharma 4-79)
--IANS (Posted on 20-12-2013)