It was a must-win match for the Black Sticks after their disappointing 2-0 loss to Korea in their Olympic opener which seriously threatened their semifinal aspirations.
They probably need at lest two wins and a draw from their final three pool games to progress and that will be tough against both the Netherlands, whom they play on Friday night (NZT), and Germany.
New Zealand were much better against India, but the match was marred by an ugly incident when Couzins was clipped around the head by India's Sandar Singh.
It wasn't a strong blow with Singh's hockey stick but the Indian appeared to mean it after their sticks became entangled and the umpires took a dim view of it and yellow carded him as James' tune Sit Down rang out around the stadium.
Couzins was later accidently bumped on the nose and went off for some treatment but returned to steer his side to their first win at these Games.
The 31-year-old was fine. In fact, he was more worried about what his teammates might say about the way he reacted to being struck.
"It was a pretty solid football dive when I saw it on the big screen replay," he said. "I'm sure the boys will give me a bit of grief but he shouldn't have had his stick there. He did the right thing and came and apologised to me after the game. It's fine.
"You get them every now and again. I think sometimes it's part of the game."
It was the low point of an otherwise good game. New Zealand were excellent in the first half apart from the first two minutes when they went behind to a Sandeep Singh drag flick.
They played with pace and good control and capitalised through a drag flick to Andy Hayward, penalty stroke to Phil Burrows and cool finish by Nick Wilson after some good work by Shea McAleese inside the circle.
But they failed to kick on in the second spell and allowed India to dictate much of the tempo even though India had two players sin-binned.
"In the second half we let them off the hook a bit," coach Shane McLeod said. "We needed to finish them but let them back in the game.
"At halftime we were trying to accumulate a few more goals. I thought it was a little bit of a missed opportunity to score a couple more goals because goals could come into it. I think we are in a pool where a few teams can beat other teams. It's going to go a little bit funny over the next few days.
"We have to beat Holland to get the three points back we lost in the first one and then we are kind of back on track. It's an easy thing to say because we will have to play well.
"It's still job not done but the guys will be getting up and feeling a lot better about themselves than they were two days ago. It's been hard to put that [defeat to Korea] aside and was eating away at them. That fear of losing is a hell of a thing but our Olympics started today."
New Zealand 3 (Andy Hayward 13, Phil Burrows 24, Nick Wilson 29), India 1 (Sandeep Singh 2). HT: 3-1.
