Chasing a target of 121, the Royals won their third consecutive match with 3.3 overs left to spare as opener Ajinkya Rahana (62 not out) and wicketkeeper batsman Sanju Samson (50 not out) guided the team home to finish.
Put in to bat, the Perth Scorchers lost their second match in three outings, as they never really got their act together, losing wickets right from the start of their innings.
Unfortunately for the Australian side, who cannot qualify for the semis anymore, their highest partnership was a mere 33 for the third wicket between skipper Simon Katich (12) and Adam Voges (27), who was also the top scorer.
With five batsman walking back to the pavilion having scored only in single digits, the Australian side crumbled and were bowled out for 120 in 20 overs.
Right arm medium pacer Kevon Cooper was the pick of the bowlers having bowled brilliantly and clinched 4/18 from his four overs. Pacer James Faulkner and leg spinner Pravin Tambe chipped in with two wickets each while all-rounder Shane Watson scalped one.
In response, the Rajasthan Royals' batsmen were in top form after an early jolt. Skipper Rahul Dravid was bowled by Jason Behrendorff on the fourth ball of the innings for a duck.
But thereafter it was a smooth ride for the home team as Rahane and Samson scored half centuries and saw their way through, taking the team through to the last four stage.
Mumbai's Rahane scored five boundaries and two sixes in his 53-ball knock while Samson sent the ball past the boundary rope seven times in his 42-ball innings.
There wasn't much available for the visiting team bowlers as only Behrendorff managed to scalp a wicket.
--IANS (Posted on 30-09-2013)