Pandya made his intent clear when he thumped three fours in an over of Vernon Philander. That is something for all the batsmen, starting at the very top.
Philander was given Man of the Match for his breathtaking match figures of 9/75.
The teams are meeting in a three-test series this month with matches in Pretoria and Johannesburg to come.
South Africa were set to resume their second innings on 65 for two, a lead of 142 on what is a lively wicket offering plenty of assistance to the seamers.
That would only be increased by 66 by the time India claimed the final eight wickets to dismiss their hosts for 130.
Bhuvneshwar Kumar picked up two, while Mohammed Shami and Jasprit Bumrah took three wickets each to destroy the South African batting line up.
All-rounder Hardik Pandya (2/27), who grabbed a couple of wickets on the second day, however could not add any more wicket to his kitty.
Shami further dented South Africa as he removed Vernon Philander.
India were under no pressure to score quickly when their second innings started immediately after lunch.
For a brief period, Murali Vijay and Shikhar Dhawan started off well with caution.
Dhawan was the first one to be back in the hut after being caught at gully by substitute fielder Chris Morris off a steeply rising delivery from Morkel.
Morkel then came back to reduce India to 39/3 after No.3 Cheteshwar Pujara (4) nicked an nearly unplayable length delivery back to the stumper Quinton de Kock. Wicketkeeper-batsman Quinton de Kock hit 43 off just 40 balls, and the tailenders all chipped in.
In his very next over, the pacer jolted India with the wicket of Sharma, who dragged a good length delivery on to his stumps.
After Philander, Kagiso Rabada struck twice to make it 82/7 for India.
Morne Morkel and Kagiso Rabada also threatened consistently on a pitch that offered seamers assistance throughout‚ and together they sent India packing for 135 just more than an hour after tea.
India's quicks had the first say, though, as Kumar exploited the generous bounce, swing and seam movement at Newlands that is normally created to play into South African hands.
Steyn sustained a heel injury while bowling on Saturday by stepping awkwardly into a foothole and has been ruled out of the rest of the series and for up to the next six weeks.