Rajasthan Royals 131-4 (20 overs) Rahane 62, Samson 26, beat Sunrisers Hyderabad 127-5 (20 overs) Morgan 27, Kulkarni 2-9, by six wickets.
Australian all-rounder James Faulkner struck Praveen Kumar for four from the final delivery of the game to help the Rajasthan Royals remain unbeaten in the 2015 Indian Premier League.
Chasing just 128, the Royals seemed to be strolling to victory before some tight death-bowling meant they took up all 120 deliveries to reach their target.
On a bowler-friendly pitch, the Royals elected to field first and it paid off as they restricted their hosts to 35-3 thanks to a couple of early wickets from Dhawal Kulkarni.
Hyderabad fought back in the middle part of their innings, with English pair Ravi Bopara and Eoin Morgan scoring 23 and 27 respectively.
43-year old Pravin Tambe picked up 2-21 for the Royals from his four overs, including the wicket of Morgan, to continue his fine start to the tournament.
Having posted a relatively low total, the Hyderabad bowlers did not get the early wickets they needed, with Ajinkya Rahane (62) and Sanju Samson (26) adding 64 for the first wicket as they edged towards victory.
Rahane was the mainstay of the Royals innings, with his 62 from 56 propelling him to the top of the leading run scorers in the competition to date, before he was dismissed with eight balls remaining in the match.
It was then left to Faulkner and Stuart Binny to finish things off for the visitors, and they did so with Faulkner living up to his nickname of "the finisher" as he flayed Kumar through the off-side for the match winning runs.
Rajasthan's fourth straight win moves them four points clear at the top of the league table, with Hyderabad down in sixth with one win from their opening three fixtures.