The two tailenders put on an unbroken stand of 30 for the ninth wicket to lift the home side to 226-8 in the 45th over after England had once again struggled with the bat to be dismissed for 222.
Iyer is not part of India's T20 squad, which will play five matches in Australia that will serve as a tune-up for the T20 World Cup in India and Sri Lanka in February-March.
Sinner, looking to take advantage of rival Carlos Alcaraz's shock second-round loss to Cameron Norrie, extended his winning streak to 24 successive matches on indoor hard courts.