But the hosts, who are still trailing by 125 runs, were dealt a savage blow with the last ball of Friday's play when their batting great Virat Kohli fell for 70.
Resuming on 3-180 at a sun-drenched M Chinnaswamy Stadium, the tourists rode Ravindra's spectacular 134 and Tim Southee's 65 to turn the screws on the hosts, who had collapsed to 46 all out on the opening day and are desperate to avoid a first home defeat against New Zealand since 1988.
New Zealand celebrate the key wicket of Virat Kohli at the end of the day. (AP PHOTO)
India were still staring at a daunting challenge despite a much more assured performance in their second innings, with Sarfaraz Khan still there on 70.
But the loss of Kohli was a huge blow after he had gone past 9000 Test runs.
Earlier, Rohit Sharma had made 52 and opening partner Yashasvi Jaiswal 35, but the dismissals of that swashbuckling duo had left India ill at ease.
Kohli then helped settle the nerves in the company of Khan and was handed a lifeline when Ajaz Patel dropped him at slip in the evening session.
But Kohli failed to make the most of the reprieve, edging one to wicketkeeper Tom Blundell off Glenn Phillips at the end of the day.
The high-scoring day had belonged to New Zealand with Ravindra's knock putting his team in a commanding position.
Born in Wellington to parents hailing from the south Indian city of Bengaluru, Ravindra reached his second Test ton with a swept boundary off Ravichandran Ashwin to draw huge cheers from an adoring home crowd.
"It was obviously special having my dad in the crowd. It's massive. A lot of family were watching the game, probably at the stadium and at home on TV," Ravindra said.
"I know they're very proud and it makes me happy that they were able to watch a relative play in their hometown. It's just very cool. I know dad and mum will be very proud.
"I'm 100 per cent Kiwi but it's nice to have that Indian heritage, based here in Bengaluru."
The allrounder hit 13 fours and four sixes, and forged a 137-run partnership with Southee for the eighth wicket.
The hosts had been bowled out for their worst total on home soil in the first innings on Thursday after the opening day was washed out.
Daryl Mitchell departed for 18 on Friday morning, finding Jaiswal at gully with a careless shot against Mohammed Siraj, while Jasprit Bumrah had Blundell (5) caught at slip by KL Rahul.
The great Kohli departs after losing his wicket in Bengaluru. (AP PHOTO)
It was the introduction of spin that troubled the Black Caps most, Ravindra Jadeja shattering the stumps of Phillips (14) to leave them on 6-223.
Matt Henry (8) perished in a similar manner after smashing a couple of boundaries as Jadeja claimed his third wicket, but New Zealand steadily clawed their way back.
Southee eventually fell to Siraj shortly after lunch, but the former captain had already done plenty of damage with five fours and four sixes in his defiant knock before the innings came to an end when Kuldeep Yadav struck twice.
After trapping Patel lbw, the leg-spinner was hit for six by Ravindra which took New Zealand past 400 but he then had the left-hander caught as he attempted another big one.
