The in-form Shubman Gill made 45 off 34 balls at the top of the order, while David Miller struck a 30-ball 46 at the Narendra Modi Stadium.
Abhinav Manohar chipped in with a brisk 27 off 13 deliveries.
In reply, RR completed the task in 19.2 overs. RR skipper Sanju Samson smashed 60 off 32 balls, while Shimron Hetmyer blazed away to an unbeaten 26-ball 56.
Mohammed Shami picked up three wickets for GT.
Brief scores:
Gujarat Titans: 177/7 in 20 overs (Shubman Gill 45, David Miller 46; Sandeep Sharma 2/25).
Rajasthan Royals: 179/7 in 19.2 overs (Sanju Samson 60, Shimron Hetmyer 56 not out; Mohammed Shami 3/25).
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