Ben Stokes smashed a quickfire half-century inside the powerplay to set up the chase. With this loss, three teams - RR, KKR and KXIP - are on 12 points making it an interesting race for the playoffs.
Rajasthan rode on a blistering 107 by Stokes and an equally aggressive 54 by Sanju Samson to overhaul a 196-run target set by defending champions Mumbai Indians with 10 balls to spare on Sunday.
The Capitals had beaten RR by 46 runs last week and Steve Smith's men will look to return the compliment when they meet for the second time in the tournament