Rabada's 3-25 helps Gujarat thrash Chennai in IPL
Pace bowler Rabada struck twice in his second over to set the tone for his team's domination as they restricted Chennai to 158-7 at the M.A. Chidambaram Stadium.
Sai Sudharsan hit 87 off 46 balls to steer Gujarat home with 20 balls to spare as they bounced back after two defeats to move to fifth spot in the 10-team table.
The top four teams at the end of the league stage will advance to the playoffs.
Sudharsan and Shubman Gill, who made 33, laid the foundation of the chase with a 58-run opening stand.
Afghanistan spinner Noor Ahmad struck in the seventh over to have Gill stumped thanks to Sanju Samson's quick glovework as he removed the bails with the batters' foot centimetres off the ground.
Sudharsan stood firm and put on a partnership of 97 with Jos Buttler, who made an unbeaten 39.
Dewald Brevis took a stunning catch in the deep to dismiss Sudharsan off Akeal Hosein with Gujarat needing four for victory and Buttler then hit the winning six.
Rabada was ably supported by fellow quick Mohammed Siraj (1-23) to dent Chennai with regular strikes despite an unbeaten 74 by skipper Ruturaj Gaikwad.
Rabada stood out with his pace and accuracy that first got the in-form Samson caught behind for 11 and three balls later dismissed Urvil Patel for four.
Siraj got Sarfaraz Khan, who came in as impact substitute, for a first-ball duck and the batting slipped further when Brevis departed for two.
Gaikwad played a defiant knock and reached his first fifty of the season with help from Shivam Dube, who made 22, Kartik Sharma (15) and Jamie Overton (18).
But the effort was not enough as Chennai suffered their fifth defeat in eight matches.