It was a resounding first win as full-time captain for the 32-year-old, who replaced Tim Southee earlier this month.
India skipper Rohit Sharma took positives from the way his side battled back in the second innings, as they attempted to become the first team to win a Test after conceding a first-innings lead of more than 350.
“We didn’t think we’d be 46 all out but due credit to New Zealand – it set us back and games like this will happen,” he said.
Sarfaraz Khan’s 150 and 99 from wicketkeeper Rishabh Pant helped India to 462 in their second innings to give the home bowlers a small total to defend on a final-day pitch that had to be covered overnight due to rain.
And Bumrah gave India a glimmer of hope when he removed Latham lbw with the second ball of the day.
He then trapped Devon Conway lbw after a successful review, but that was India’s last breakthrough.
First-innings centurion Ravindra hit six fours in his unbeaten 39 and was named player of the match, while Young hit the winning runs with his seventh four as he finished on 48.
“We have got to take the good things forward,” added Rohit, with the second Test scheduled to begin in Pune on Thursday.
“We’ve been here before, conceding home losses, these things happen. We know what it takes and will give it all in the next two Tests.”
India have history on their side, having won 18 consecutive Test series on home soil, stretching back to 2012.
