The visitors posted a challenging total of 270 for six and made early inroads into the White Ferns batting line-up.
But Kerr scored an undefeated 119 off 135 balls to guide the home team to victory.
The White Ferns lead the series 2-0 and will feel good about having responded to the pressure.
Opener Sophie Devine rattled on a quick 33. But the in-form Suzie Bates fell for 16 and classy left-hander Amy Satterthwaite was dismissed for a golden duck.
The White Ferns were struggling at 55 for three but Maddy Green and Kerr put on 128 for the fourth wicket.
Green scored 52 before she was caught out off the bowling of Poonam Yadav.
But Kerr pushed on. Veteran keeper Katey Martin chipped in with 20.
When she perished in the 46th over, the match was still in the balance.
The White Ferns needed 32 runs off 29 balls.
Hayley Jensen could not get going but Jess Kerr joined her sister and clobbered the winning runs from the last ball of the penultimate over.
Despite the shaky start, Melie Kerr said she backed herself and her teammates to chase down the target set by India.
"I think the good thing was we got off to a bit of a flier, so there was not run rate pressure.
"Maddy and I knew we just had to rebuild and keep some wickets in hand and that by playing good cricket shots we were going to score at a good rate naturally.
"I guess you could say we timed it perfectly."
Finishing her innings alongside her sister Jess was the icing on the cake for Kerr, who was named the player of the match.
"It was nice to get the win and nice to finish it off with Jess out there."
Earlier, India made a promising start through openers Sabbhineni Meghana and Shafali Verma (24), who put on 61 from 11.1 overs.
Yastika Bhatia kept the moment going with 31 from 38.
Meghana’s departure for 49 from 50 balls was critical. And Harmanpreet Kaur (10) mistimed a full toss to gift 17-year-old left arm spinner Fran Jonas her first international scalp.
That mistake completed a rapid descent from 110 for one to 135 for four.
India should have suffered a further setback but Brooke Halliday muffed a chance in the outfield.
Richa Ghosh got away with it and made the White Ferns pay.
She launched a towering six over the head of bowler Rosemary Mair to close in on her maiden half century.
The shot also brought up the team 200.
She eased the ball into the off side to bring up the milestone.
Mithali Raj had been ticking along quietly at the other end as the partnership grew.
The pair added 108 before Ghosh was dismissed for 65 from 64 balls.
Raj remained undefeated on 66.
But the day belong to Kerr, who has really shone with the bat this season.
Great timing with the World Cup getting under way in New Zealand next month.
