Grandhomme got out with 10 balls to spare but the final push by Ross Taylor and Daryll Mitchell helped New Zealand post a total of 212 in 20 overs.
A New Zealand XI has beaten Bangladesh by two wickets in a one-day match at Lincoln.
Just like the first T20I, New Zealand openers Colin Munro and Tim Seifert gave their side a wonderful start.
It took a lightning fast stumping by MS Dhoni off the bowling of Kuldeep Yadav to break the partnership.
Meanwhile, Indian bowlers too showcased an impressive performance, with Krunal Pandya bagging three wickets and Khaleel Ahmed, Hardik Pandya and Bhuvneshwar Kumar sharing four wickets among themselves to restrict the hosts for 158.
India, who came into the three T20Is on the back of their crushing 4-1 win in the five-match ODI series against New Zealand, failed to continue their dominance and slump to a humiliating 80-run defeat in the opening T20I at Westpac Stadium in Wellington.
Apple releases bug fix for embarrassing security flaw that allowed FaceTime eavesdropping
Users can update their software by going to " Settings " on their device, choosing " General " and selecting " Software Update ". You will need Wi-Fi access and your battery to be charged above 50 percent, or the device will need to be connected to a charger.
Dinesh Karthik and Krunal Pandya were only able to take 11 runs off it, with Karthik's six from the final ball in vain.
Scott Kuggeleijn took the Black Caps' other wicket - his first of the series.
What followed next were two short but exhilarating innings by Rishabh Pant and Hardik Pandya.
Karthik finished on 33 runs off 16 balls while Krunal finished on 26 runs off 13 balls.
Colin Munro's explosive 72 set New Zealand up for victory with a four-run win over India in a cliff-hanger finish to Sunday's Twenty20 match in Hamilton, handing the hosts a 2-1 series victory.
The 1-2 series defeat was India's first T20I series loss after winning eight and drawing two.