Needing 17 off the final over, Hyderabad pace bowler Sandeep Sharma witnessed Samad get dropped on the first ball and then got him caught on the sixth delivery which turned out to be a no ball which abruptly cut short Rajasthan's victory celebrations.
With another four needed to win on the final ball, and three to take the game into the super over, Hyderabad had the last laugh as Samad smashed a straight six in his seven-ball 17.
Hyderabad slipped to 174-5 when New Zealand's Glenn Phillips turned the game on its head with a seven-ball 25 that infused life into the chase.
Phillips had come into the Hyderabad team for the under-performing big England buy Harry Brook while England's Joe Root played his first game of the season for Rajasthan.
The victory was set up by key knocks from Abhishek Sharma (55), Rahul Tripathi (47) and Heinrich Klaasen (26) in the team's highest ever chase in IPL.
Yuzvendra Chahal's bowling figures of 4-29 went in vain after he picked up key wickets including two in one over.
Rajasthan posted 214-2 after a destructive second-wicket stand of 138 between Jos Buttler, who smashed 95 off 59 deliveries, and skipper Sanju Samson, who hit a 38-ball 66.
Buttler started slowly with his first 20 coming at run-a-ball but soon changed gears to bring up his fifty.
Seam bowler Bhuvneshwar Kumar denied Buttler his century to get him out lbw, but Samson finished off the innings in a 17-run over.
