On their match vs Chennai Super Kings, KKR was left reeling at 31/5 but Andre Russell and Pat Cummins played knocks of 54 and 66 to keep Eoin Morgan's side in the hunt.
While Jos Buttler's direct hit ended Gill's knock with KKR scoring 25 runs in the powerplay, KKR kept losing wickets at regular intervals and got reduced to 61/4 at the halfway mark.
Punjab has lost their last three games while defending champions Mumbai are also coming after a loss against Delhi Capitals.
Kohli is leading the IPL highest run-getter chart followed by Suresh Raina, Shikhar Dhawan, David Warner and Rohit Sharma.
The 30-year-old left-arm pacer did not feature in the last two games of SRH and he just played two games this season, taking two wickets.
RCB never looked in any tearing hurry and yet the target was achieved in only 16.3 overs with all 10 wickets intact.
Sunrisers have lost three matches on the trot at the MA Chidambaram Stadium track here, which has the reputation of aiding the spinners.
KKR has made two changes as Kamlesh Nagarkoti and Sunil Narine come in for Harbhajan Singh and Shakib Al Hasan.
Last week, Ben Stokes was ruled out of the remainder of the IPL due to a finger injury and he has been sidelined for up to three months.
Under Smith's captaincy, the inaugural edition champions RR finished last in the last IPL in the UAE, where the star Australian batsman played all the 14 league matches and scored 311 runs.