Abhishek raised his century in 40 balls as he roared, punched the air and waved a piece of paper with a message “this one for the orange army” — the colour of Hyderabad.
Punjab left-arm quick Arshdeep Singh sent back Abhishek, who hit 14 fours and 10 sixes, with 24 to win and Heinrich Klaasen got Hyderabad home with an unbeaten 21 off 14 balls.
Earlier Iyer struck his fastest IPL fifty in 22 balls before Stoinis hammered an 11-ball unbeaten 34 to boost the Punjab total.
New batting sensation Priyansh Arya and partner Prabhsimran Singh handed Punjab a quick start as the two smashed 53 runs in the first three overs.
Previous-match hero Arya, a left-hander known for his six-hitting prowess, departed after his 13-ball 36 and Prabhsimran went out next, for 42, with Sri Lanka’s Eshan Malinga getting his first IPL wicket on debut.
Iyer took on the bowlers and his quick fifty was better than his 23-ball half-ton for Kolkata Knight Riders against Hyderabad last year in qualifier 1.
Medium-pace bowler Harshal Patel struck regular blows including two in one over when he got Glenn Maxwell bowled for three and Iyer caught out at backward point. Patel returned figures of 4-42.
But Stoinis hammered pace spearhead Mohammed Shami for four straight sixes to finish off the innings in a 27-run last over.
Shami conceded 75 runs form his four wicketless overs to return the second most expensive spell in IPL after Rajasthan Royals’ England import Jofra Archer had 0-76 in the second match this season.