Electing to bat, the Chargers rattled up 166 for seven, relying mainly on Smith’s 47. Rohit then took three for 12 as the Royals slumped to 113.
Rohit returned figures of 3-0-12-3 after Chaminda Vaas had rocked the defending champions two early wickets at the De Beers Diamond Oval. Rudra Pratap Singh and Pragyan Ojha chipped in with a wicket apiece.
With their sixth win from 10 matches, the Chargers jumped to third spot with 12 points, swapping places with the Royals, who are now fourth (11 points from 11 matches).
Chasing a difficult target, the Royals withered against a disciplined bowling attack with none of their batsmen, excepting Swapnil Asnodkar (44), making any notable contribution.
By the 10th over, they were in trouble at 59 for three and their chase was as good as over by the time they limped to 96 for six in the 15th over.
The Royals began their run chase in the worst possible fashion. Graeme Smith (1) was struck on above his knee roll off Vaas’ first delivery of the tournament, and was adjudged leg before by Kumara Dharmasena.
Vaas, coming in for Ryan Harris, then dismissed Lee Carseldine (8), stumped by Adam Gilchrist to reduce the Royals to 19 for two.
Earlier, the Chargers struggled against disciplined bowling before Smith lifted them with a 32-ball 47 studded with four sixes.
Pathan was the most successful Rajasthan bowler with three for 34 while Jadeja bowled beautifully to chip in two wickets for 26 runs.
Smith was quiet initially but opened up towards the end, taking his side from 108 in the 15th over to 166..
He shared a 29-ball 37 with Vaas (20) for the fifth wicket and a quickfire 35 from just 14 balls with Venugopala Rao (12) for the sixth wicket. Andrew Symonds (30) and T Suman (29) were the other notable contributors for the Chargers.