Chasing 163 runs to win, Punjab's reply never really got going and they only managed to reach 136/8 in their 20 overs.
Australia's World Cup hero James Faulkner was Royals' star man was well with his innings-pacing knock of 46 runs and then taking 3/26 with the ball.
The Punjab run chase got off to the worst possible start when Virender Sehwag (0) was out first ball of their innings, edging a Tim Southee delivery to the wicketkeeper.
And their problems compounded further with the quick dismissals of Wriddhiman Saha (7) the dangerous (7).
India test opener Murali Vijay (37) was shaping up nicely to guide the team's run chase but his run out in the nonth over severely dampened their chances from which they simply didn't recover.
Earlier, Rajasthan Royals posted 162/7 against Kings XI Punjab in their 20 overs.
Faulkner (46) was the principal run scorer for the Royals while pacer Anureet Singh 3/23 was the pick of the Punjab bowlers.
Punjab captain Australian George Bailey won the toss and invited Royals to bat.
His judgement was justified by his team's bowlers as they struck as early as in the second over when pacer Anureet dismissed India batsman Ajinkya Rahane for zero.
Royals were unable to get over the early jolt and kept losing wicket at regular intervals. Skipper Australian Steven Smith (33) put up some resistance but his compatriot pacer Mitchell Johnson struck twice in the 11th over to seize the initiative and reduce Royals to 75/5 in 10.4 overs.
But the 51-run sixth-wicket partnership of Deepak Hooda (30) and Faulkner resurrected their innings and helped them post a decent total.
A minute's silence and black armbands were worn by the players, match officials and the commentators to pay tribute to the death of the legendary former Australia captain and cricket broadcaster Richie Benaud prior to the start of the match.
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