Forward Navneet Kaur scored a beautiful goal in the 57th minute off a superb pass from the right flank by skipper Rani Rampal to seal the victory for India.
This is only the third win for the Indian women's team in the three appearances in the Olympics. The first two wins came in 1980 Olympics in Moscow while in the 2016 edition at Rio de Janeiro India could manage only one draw in five matches.
Friday's win, coming after three defeats against strong opponents, has India sharing the fourth spot with Ireland, both with three points but India were placed fifth as they have an inferior goal difference -- -8 as against -5 for Ireland.
India will now play South Africa in their final League match while Ireland meet reigning champions Great Britain on Saturday.
Victory for India and defeat or draw for Ireland will move them to fourth place and put them in the quarterfinal, the stage they had aimed to achieve at the start of the Olympics. Draw or defeat for both India and Ireland will bring the goal difference into account.
But midway through the match, it looked like India would not be able to put it across Ireland considering the number of chances that they had wasted.
India started aggressively against a team ranked eighth, just one place ahead of Sjoerd Marine's squad in the ranking and dominated the first half, creating 10 penalty corners but failing to convert any.
Ireland created a goal-scoring opportunity early on in the first quarter, however, the Indian defence stood tall and deflected the ball away.
The Indians attacked soon after and made a circle penetration. However, Navneet Kaur couldn't find the back of the net after getting close to the goal.
The Indians continued to put pressure on the Irish goal and earned a penalty corner in the 9th minute but Gurjit Kaur couldn't find the back of the net.
Navneet had another chance when she went through two Irish players and took a shot at the goal, but was thwarted by the Irish defence.
India earned a number of penalty corners in the last five minutes of the first quarter, however, couldn't convert any of them.
In all, India earned 14 penalty corners but could not convert any. They also had 21 shots on the goal but only one goal to show. They made 30 attacking circle penetrations while Ireland could manage only 15.
But in the end what mattered was that India bagged three points that keep them in the hunt for a spot in the quarterfinals.
Coach Marijne said the only matter of concern was the number of chances they missed.
"The only thing we can blame ourselves for is that we didn't score enough. It's not easy to score penalty corners against Ireland, but our performance was not good on a few occasions, but we kept going.
"Getting 14 PCs in the match says a lot and I like to talk about the positives that we got those PCs. We outplayed Ireland, but you won't see it in the numbers. We kept going in the match, we didn't stop. Three minutes before time, we kept pushing and this match has also shown the quality the team has gained and I am very happy with that. And now it's all about recovery and getting ready for the next match as we have a game against South Africa in less than 24 hours."