Sudharsan slammed 82 from 53 balls (8 fours and 3 sixes) to power GT to 217-6 in 20 overs.
Among other contributors, wicketkeeper-batter Jos Buttler and Shahrukh Khan slammed 36 each.
In reply, RR skipper Sanju Samson (41 from 28 balls) and Shimron Hitmyer (52 from 32 balls) kept the visitors' hope alive until they collapsed failing to tackle GT bowlers led by Prasidh Krishna (3/24 in 4 overs).
RR were bowled out for 159 in 19.2 overs after losing momentum in the run-chase.