Though Rajasthan had almost clinched a victory, Sandeep Sharma's no-ball gave a second chance to the visitors to finish the job.
Needing four runs off the last ball, on-strike Abdul Samad slammed a six in the extra ball to take Hyderabad to 217/6 in 20 overs.
Prior to Samad's heroics, Glenn Phillips hit a much-needed 25 off just 7 balls to add fuel to Hyderabad's run-chase which was once fading out.
Abhishek Sharma (55 off 34 balls) and Rahul Tripathi (47 off 29 balls) made significant contributions to Hyderabad's total.
Earlier, Rajasthan scored 214/2 in 20 overs giving a tough challenge to the visitors.
Jos Buttler, the architect of the mammoth total, slammed 95 off just 59 balls, hitting 10 fours and four sixes.
Skipper Sanju Samson too fired with his unbeaten 66 off 38 balls.