Mystery spinner Suni Narine took 2 wickets for 28 runs in his 4-over spell.
Rajasthan skipper Shane Watson made a quick-fire 31 off 20 balls.
Karun Nair smashed 44 off 35 balls to take Rajasthan Royals to 170 for 6 against Kolkata Knight Riders.
Sanju Samson scored a 31-ball 37 before he was out to Sunil Naraine.
Robin Uthappa scored a gritty 65 off 52 balls before he fell to Shane Watson in the 15th over.
Gautam Gambhir smashed a 34-ball 54 and shared a 121-run opening stand with Uthappa.
Pravin Tambe took the first hat-trick of IPL 7 when he sent back Manish Pandey, Yusuf Pathan and Ryan ten Doeschate for ducks.