Put in to bat, Rajasthan openers Jos Buttler (41 off 32) and Yashasvi Jaiswal (32 off 20) laid the foundation with their 66-run stand in 7.4 overs.
Buttler started with a first-ball boundary, a flick it to the fine-leg fence. The Englishman then fetched his second four, off Jasprit Bumrah (1/15), a cheeky hit to the third man boundary.
Jaiswal picked his first boundary in the third over off Trent Bout (1/37), a pull to the backward square-leg boundary. Buttler, who got a life, then upped the ante. He took on off-spinner Jayant Yadav (0/37), hammering a four and then a maximum, in the fifth over.
Jaiswal too changed gears, as he struck a four and a maximum, his trademark pull-shot, off successive deliveries off pacer Nathan Coulter-Nile (0/35), as his team amassed 14 runs of the sixth over and raced to 47/0 after power-play. Buttler, who was in his elements, smashed Jayant for another six in the seventh over.
Buttler hit another maximum, this time off Rahul Chahar (2/33), but the leggie dismissed him the very next ball, having him stumped by Quinton De Kock.
Samson, started with a boundary, a cut-shot and then hit two boundaries off Krunal Pandya in ninth over, in which RR got 12 runs. But Chahar struck again, this time removing Jaiswal, as he lobbed off a return catch.
Shivam Dube (35 off 31 balls; 2x4, 2x6) and Samson, who plundered five boundaries, conjured 57 runs for the third wicket, with the Mumbaikar playing aggressive shots.
Samson also kept playing shots at will, as he hit two successive boundaries, in the 16th over off Boult, which fetched his team 14 runs.
However, Boult cleaned up Samson in the 18th over and then Bumrah dismissed Dube in the penultimate over as the Mumbai bowlers kept things tight in the last four overs. RR got 45 runs in the last five overs.