Indian batsman Ajinkya Rahane helped himself to a classy 62 after Rajastan were set 128 for victory but the Royals struggled in their reply before keeping their perfect record intact from the very last ball.
Australia opener David Warner made 21 before being run-out before the Sunrisers survived a controversial moment in the 11th over after James Faulkner thought he had got Naman Ojha out.
However, after a review, the TV umpire adjudged Australian Faulker to have bowled a no-ball leaving Royals captain and compatriot Steve Smith rather unhappy.
England one-day captain Eoin Morgan made his debut for Hyderabad but managed 27 before falling to leave the Sunrisers on 96-5.
Morgan’s international team-mate Ravi Bopara ended unbeaten on 23 to help steer his side to 127-5 after their 20 overs with Dhawal Kulkarni and Pravin Tambe snaffling two wickets apiece.
Rahane got Rajastan’s reply off to quick start by smashing 62 off 56 balls with support from opening parter??Sanju Samson (23).
However, Smith and??Karun Nair fell cheaply before??Stuart Binny and Faulkner held their nerve with the Aussie blasting four from the last ball off a wicketless??Bhuvneshwar Kumar??to win it despite Bopara taking 2-18.