Set 142 to win at a modest rate of 7.1 an over, the rookie all-rounder clubbed six fours and four sixes in an eye-catching knock to lead his side to their fourth qualifying win with 26 balls to spare.
Sussex openers Calum MacLeod and Luke Wright got their side off to a flying start by posting 61 in the powerplay, including 22 from Imran Qayyum's first over of left-arm spin.
Joe Denly gave Kent their first breakthrough soon after, grabbing a looping caught and bowled chance off MacLeod (19).
Qayyum was immediately replaced by Jack Leaning's occasional off-spin and, with Denly's leg-spin at the Pavilion End, Kent tried to keep pace off the ball, but Rawlins swept powerfully over the mid-wicket ropes for the first six of the reply.
Wright fell five runs short of his 43rd half-century in domestic Twenty20 when his back-foot flail against Calum Haggett was caught behind by Jordan Cox.
Rawlins lofted Haggett for a straight six to take Sussex into three figures and then, when Qayyum returned, took 12 off the over including another maximum, this time over mid-wicket.
The 22-year-old left-hander from Bermuda celebrated his 31-ball 50 with a fourth six, pulled off Fred Klassen, who was then sent crashing to the ropes at extra cover as Sussex sealed the win with more than four overs to spare.
Batting first after losing the toss, Kent's top four batsmen had earlier all reached double figures without going on to play a match-defining knock.
Having seen the home openers cruise to 24 inside three overs, Sussex turned the tide by introducing left-arm spin at both ends in the shape of Danny Briggs and Rawlins.
Briggs should have had Daniel Bell-Drummond, on eight, caught by Oli Robinson off a skier to mid-on but, inexplicably, Robinson allowed the chance to slip through his hands. He made immediate amends, however, diving to his left to catch a rasping Zak Crawley drive from Briggs' next delivery.
Denly clubbed three successive boundaries against Robinson to see the Spitfires through to 57 for one after their powerplay, but Bell-Drummond missed an attempted slog-sweep on 29 to be bowled by Rawlins.
Denly swept a boundary off Briggs and then slog-swept the next for the first six of the innings. But, in trying to repeat the stroke two balls later, he top-edged to third man to top-score with 32.
Rawlins had Heino Kuhn (22) caught on the run at backward square leg, then Chris Jordan hurried one past Alex Blake's outside edge to remove the left-hander's off stump.
Briggs snared Cox lbw as the right-hander missed an attempted reverse sweep to finish with three for 27 and leave Kent in trouble on 107 for six.
Leaning followed meekly, gloving an attempted pull shot against Robinson through to the keeper, forcing Kent's tail-enders to simply bat out their side's closing five overs.
Grant Stewart contributed nine before his sliced drive against Tymal Mills was caught at deep point and, as the runs dried up, Kent managed only one boundary in their last eight overs.