While the duo did not play too many big shots, they kept the scorecard ticking, with Gill cashing in on every scoring opportunity, and made sure that KKR did not lose any wicket.
KKR were momentarily put on the backfoot after Rana and captain Dinesh Karthik fell in a relatively short period.
With KKR needing a big partnership, Eoin Morgan then joined Gill in the middle.
Reigning World Cup-winning skipper Morgan played the flawless supporting role before joining the party by smacking Bhuvneshwar Kumar for a huge six in the 15 over.
KKR's record buy Pat Cummins followed up his underwhelming show in the first match with a masterful performance on Saturday, returning miserly figures of 1/19 in four overs.
Bairstow's opening partner Warner was looking in great touch until he was caught and bowled by Chakravarthy.
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Earlier, SRH won the toss and chose to bat - the first time any team has done that this season. Apart from Chakravarthy, Andre Russell was the third wicket taker for KKR, having accounted for the wicket of Manish Pandey.
Saha then perished in the final over as KKR managed to restrict SRH to 142/4.
Gill finished his 5th IPL fifty from 42 balls and struck 2 6s and 5 fours in his 62- ball knock, while Morgan nailed 2 6s and 3 fours throughout the 29 balls he dealt with, finishing up his group's detailed triumph by striking T Natarajan for 6 and 4 off succeeding balls in the 18th over. "I didn't have to tell Gill a great deal to be honest. he's attractive to watch, has a good bat swing, very languid style.", Morgan said.
Earlier, Hyderabad had been restricted to 142 for four after David Warner elected to bat first, which broke the sequence of teams electing to field after winning the toss in this IPL.
SunRisers Hyderabad lost opener Jonny Bairstow, who is celebrating his 31st birthday today, cheaply for five runs.
"Patty Cummins, as he does, (bowled) Test match line and length", said Warner, who made 36.