Drag-flickers VR Raghunath (15th minute) and Rupinder (27th, 49th) converted three out of seven penalty corners India earned in the match to secure their first win in an opening clash at the Olympics since Sydney Games 2000.
Ireland gave India a run for their money, especially in the second half, finding the net twice through Jermyn John (45th) and Conor Harte (56th) at the Olympic Hockey Centre.
From the word go, the Indians started on an attacking note and put pressure on the Ireland citadel with relentless raids.
The Irish, on the other hand, were happy to fall back and defend in numbers, depending mainly on counter attacks to stun their opponents.
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India's domination can be gauged from the fact that they earned as many as six penalty corners in the first two quarters as against Ireland's two.
Then just a second from the end of the first quarter India earned three more back-to-back penalty corners, the last of which was ably converted by VR Raghunath with a powerful low flick to the right of the Irish goalkeeper.
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Ireland earned another short corner three minutes later, but the try went wide.
The Indians managed to get another penalty corner in the final minute of the second quarter but wasted the opportunity as they went into the breather with a two-goal cushion.
After the change of ends, Ireland looked a completely different side as they took the initiate and pressed the Indian defence hard in search of goals.
The Irish, featuring in hockey at the Olympics after a hiatus of 108 years, in the process secured two penalty corners in a span of two minutes and John scored his first international goal from the second opportunity to reduce the margin to 2-1.
But Ireland did not sit back and put continuous pressure thereafter, managing to break the resolute India defence in the final 10 minutes of the match.
Under pressure the Indian defence looked out of sorts and in the process conceded four penalty corners, the third of which resulted in a goal for the Irish.
Conor Harte scored from Ireland's seventh penalty corner after the initial effort was saved by Indian goalkeeper PR Sreejesh.
The Indians, thereafter, played defensive hockey and concentrated on holding possession of the ball to secure full points from the match.
India will next play reigning Olympic champions Germany on August 8.
Earlier in the first match of Pool B, Argentina held London Olympics silver medallist Netherlands to a 3-3 draw.