The captain reached his maiden T20 hundred after 42 balls on Tuesday — tied for the sixth-fastest century by an India player in the format — as the hosts finished with 2-172 in 14.4 overs, chasing West Indies' 171 after they were bowled out with five balls left of their allocation.
Iyer hit six sixes and 10 fours, while Ishan Kishan scored 37 not out, as the duo put on 137 off 67 balls for the third wicket.
Shai Hope (52) and Sherfane Rutherford (56) had earlier hit half-centuries for the visitors to help them recover from 8-135, but it always looked to be an under-par score against the T20 world champions.
India had won the toss and opted to bowl, with batting allrounder Naman Dhir making his T20I debut for the hosts.
Chasing 172, India lost their in-form batters in the powerplay, Abhishek Sharma scoring 21 off 10 balls, before holing out off Roston Chase, and Sanju Samson dismissed for 11.
India made 2-62 in the powerplay, as Kishan and Iyer helped the innings recover to 2-102 at the halfway mark.
Iyer reached 50 off 28 balls with eight fours and then accelerated, scoring his next 50 off only 14 balls including six sixes.
Iyer was 72 not out off 36 balls at the start of 14th over — he hit two sixes off Matthew Forde and then was dropped at long on on the third delivery. He then hit two more sixes to reach his maiden hundred in style.
This was all after West Indies had made a poor start, Arshdeep Singh bowling Kamil Pooran for 12 and Shimron Hetmyer getting run out for five with Iyer involved in the dismissal.
Axar Patel bowled Rovman Powell for a three-ball duck and West Indies were down to 3-44 in the powerplay.
Hope and Rutherford added 63 off 35 balls to rescue the innings but Dhir (3-31 in his four overs) grabbed his maiden T20 wicket in the 12th over as Hope was out caught at midwicket.
West Indies continued to lose wickets in the lower-middle order, and only Rutherford's three sixes helped them past the 170 mark.
The second match will on Friday in Ranchi.
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