Ravindra crafted a career-best 240 as the home side were dismissed for 511, before the tourists' inexperience was exposed as they were reduced to 80-4 at stumps on day two.
A Proteas team featuring six players new to international cricket will resume on Tuesday facing a deficit of 431 runs, after four wickets tumbled in the space of 14 overs late at Bay Oval.
Seamer Kyle Jamieson took 2-21 and could have had a third if Matt Henry had held a chance in the outfield to remove David Bedingham.
Bedingham and Petersen survive
Instead, Bedingham was unbeaten on 29 at stumps, alongside Keegan Petersen on two.
The pair are the only members of South Africa's tour squad who played in the drawn home Test series against India a month ago, with the bulk of their first-choice players having committed to play in the country's domestic Twenty20 league.
Opener and captain Neil Brand was Jamieson's first victim, caught behind for four, before fellow-debutant Raynard van Tonder departed in the same over, trapped leg before wicket for a two-ball duck.
Edward Moore (23) ballooned a Henry bouncer to a close fielder before Zubayr Hamza (22) edged a ball from spinner Mitchell Santner into his stumps.
South Africa batting coach Imraan Khan conceded his team would need to fight their way out of a hole.
"Fair play to the Kiwis, I thought they executed quite nicely, in particular Jamieson," Khan said.
"We've got to knuckle down, create some partnerships through the rest of the innings and hopefully we can put on a good performance tomorrow. We've got two fantastic players who are in at the moment.”
Earlier, New Zealand's last five wickets fell for 38 as they pushed for quick runs.
One of them was Ravindra, whose 366-ball knock was a dramatic turnaround in the longest format, having never scored more than 18 in six previous Test innings.
He had been selected as an all-rounder in his three Tests and said he felt more comfortable as a specialist batsman coming in at number four.
"A different role probably helps, you feel more at home in that batting role," he said.
"And also spending time with the guys in the team. I've been in the environment for almost three years now so you gain a lot.
"You always want to do well, to feel a belonging.”
The left-hander, who began the day on 118, struck 26 fours and three sixes, with stroke-making reminiscent of his prolific efforts at last year's 50-over World Cup in India.
Ravindra was bowled trying to pull left-arm spinner Brand, who went on to claim figures of 6-119.
Brand became the first South African spinner to take six wickets on Test debut and his figures are the fourth best by a Proteas captain.
His most spectacular effort was a sharp caught-and-bowled to remove Daryl Mitchell for 34 and end a 103-run partnership with Ravindra for the fourth wicket.
That followed a stand of 232 between Ravindra and Kane Williamson, who was caught on 118 trying for a big hit off Ruan de Swardt.