Riyan Parag (76) and Sanju Samson (68 not out) slammed cracking fifties and shared a 130-run partnership to power RR to a challenging 196 for three.
In reply, GT looked down and out at 157 for six in 17.3 overs but Rashid Khan (24 not out) and Rahul Tewatia (22) took the team home on the last delivery of the innings.
GT skipper Shubman Gill top-scored with a 44-ball 72.
Brief scores:
Rajasthan Royals: 196 for 3 in 20 overs (Riyan Parag 76, Sanju Samson 68 not out; Rashid Khan 1/18).
Gujarat Titans: 199 for 7 in 20 overs (Shubman Gill 72, Rashid Khan 24 not out; Kuldeep Sen 3/41).