Clark’s electrifying knock gave Sussex a flying start – the left-hander smashed Matt Milnes for three sixes in quick succession and Tom Rogers’ second over cost 30 as the visitors raced to 92-0 in the powerplay.
But once Clark was caught in the deep to provide former Sussex off-spinner Bertie Foreman with his first Spitfires wicket, Kent clawed it back through fellow debutant Forrester, whose career-best figures included a double wicket maiden.
James Coles (28 from 26) and ex-Kent batter Jack Leaning (30 from 25) did their best to regain momentum but, despite a late flurry by Danny Lamb, with an unbeaten 22 from 12, the visitors fell just short of 200.
Kent kept the required rate under control throughout, with openers Tawanda Muyeye (26 from 15) and Daniel Bell-Drummond (29 from 19) scoring rapidly before Crawley and Sam Billings added 55 from 32.
Spitfires skipper Billings (28 from 17) miscued Fynn Hudson-Prentice and was caught at backward square, but Forrester immediately settled in with successive cover boundaries as Crawley stepped up the pace.
He was given a life on 42, drilling Danny Briggs to long-on – only for Tom Alsop to fumble the ball across the rope – and capitalised by pummelling Lamb for three sixes in an over before Forrester thumped Tymal Mills to the fence to seal victory with 10 balls to spare.