The Bermudian took 2-25 with the ball as he and spin-partner Danny Briggs (3-27) and the Sussex seamers reduced Kent to a below-par total of 141/8 - before the all-rounder shone with the bat, hitting 62 not out to seal a superb win for the Sharks.
Kent got off to a flier in the powerplay as Daniel Bell-Drummond and Zak Crawley took them to 25/0 from after three overs.
Sussex should have had seen the back of Bell-Drummond the following over when the opener mistimed a shot off Briggs, but Ollie Robinson was unable to hold on what looked to be a simple catch. However, Robinson, the only Sharks change to the team for their 13-run over Hampshire last week, immediately made amends when he took a tumbling catch to remove Crawley for 16, an opportunity a lot harder than the ball before.
Some tight bowling from the Sharks looked like it was going to prevent Kent from quickly building on their good start, but 17 runs came from the sixth over including three consecutive boundaries from Joe Denly to ensure the Spitfires ended the powerplay on a high.
The Sharks halted the hosts progress once again just two overs later with Bell-Drummond bowled by Rawlins for 22, the Kent captain swatting across the line and having his stumps rearranged.
Luke Wright had been at the heart of both dismissals as the Sharks skipper mixed his bowlers up and these changes brought about a collapse which saw Kent lose seven wickets for 35 runs with Briggs starting the rot by removing Denly for 32, caught by Robinson after the England batsman top-edged a sweep of the leg-spinner.
Rawlins picked up his second wicket the following over when Heino Kuhn picked out Callum MacLeod on the deep square leg boundary and had to depart for 22 before Chris Jordan picked up his first when he knocked the off stump of Alex Blake out the ground with the big-hitting Kent batsman having to depart for three.
The Spitfires lost Jordan Cox for one the following over, the 19-year-old keeper was trapped leg-before by Briggs.
Sussex dismissed Jack Leaning two overs later for three after the batsman feathered a catch to keeper Ben Brown off Robinson before Grant Stewart was out for nine the next over, caught by George Garton in the deep off Tymal Mills.
Callum Haggett and Imran Qayyum were able to stop the collapse and see out the remaining overs, with the pair dragging Kent to 141/8 in the process.
In reply Sussex got off to a superb start, Wright and MacLeod putting on a half-century stand in just 5.3 overs, the former bringing it up via three consecutive boundaries off Qayyum as he took the slow left-armer’s first over for 20 runs.
The Sharks ended the powerplay at 61/0 but lost their first wicket just two balls later when MacLeod was dismissed for 19 after he mistimed a pull shot off Denly and saw the ball loop back to the leg-spinner for a simple catch.
Rawlins picked up where MacLeod left off smashing 11 runs out of a 12 run over from Denly but soon the Bermudian had a new partner, Wright edging behind to Cox for 45, Haggett getting the breakthrough that gave the hosts a glimmer of hope.
Ravi Bopara and Rawlins calmed any Sussex nerves that may have been creeping in as a 58-run partnership sealed the game for the Sharks with Rawlins striking three successive boundaries to win the game for the Sharks by eight wickets, the 22-year-old the star of the show as he made his third T20 fifty, finishing on 62 not out.
Skipper Wright said: "After the great start Kent had I thought that maybe they believed they needed a score of about 180 to 200, but it really wasn’t that type of wicket today. Getting those wickets in the middle overs helped us to drag it back and it was great for us that Delray got a couple of wickets too.
“I’ve been trying to give him more of a bowl in this and he helped us to strangle them run-rate wise in the middle overs. At the halfway stage, we were absolutely delighted with a display in the field. When you’re chasing 140-odd, the only way you’ll ever be in trouble is if you’re 20 for two after the powerplay, so I made a decision to break the back of it in the first six overs.
“I’d spoken to Danny Briggs, who told me the ball wasn’t spinning much from the Nackington End, so when the left-armer [Imran Qayyum] came on, I took my moment to really have a go. We were clinical all the way through.
“We’ve been asking Delray to have a better tempo about his batting. He sometimes goes at it so hard that he tends to give his wicket away. It was so pleasing to se him bat the way he did here. He looked like a superstar out there and we know he can go on and be the international player he aspires to be.”
The win for Sussex sees them leapfrog Kent and Surrey to go top of the South Group table with four games to go.