Rinku, who made his international debut in the first T20I but did not get a chance to bat, chipped in with a fine cameo of 38 off just 21 balls in his debut innings.
The left-handed Rinku got off to a sedate start before he fired on all cylinders and went hammer and tongs against Ireland bowlers.
From 15 off 15 at the end of the 18th over, Rinku smacked his next five balls for 4, 6, 6, 1, 6, before Mark Adair ended his entertaining stay at the crease.
Talking about the match, Ruturaj Gaikwad and Sanju Samson played impressive knocks to take India to a healthy 185 for 5.
Gaikwad made 58 off 43 balls and shared a crucial 71-run partnership with Samson, who made a quick-fire 26-ball 40.
Though it appeared that India were losing some momentum in the back-end of the innings, Rinku found his groove in a late burst and with Shivam Dube being 22 not out, the duo hit 42 runs in the last 12 balls to take India past 180.