Fine bowling performances from Danny Briggs (two for 19) and Will Beer (two for 17) restricted the home side to just 140 from their 20 overs, with Ben Stokes top-scoring with 34 after the Jets opted to bat first.
Although Durham made early inroads, Laurie Evans and Delray Rawlins were outstanding, with the former notching a composed half-century to guide Sussex to a convincing victory.
The Jets made a blistering start to their innings with Stokes and Graham Clark at the crease.
Stokes led the assault, hitting four boundaries off Jofra Archer's first over before Chris Jordan showed his experience, sending a slower ball down to dismiss Clark.
Sussex began to dry up the runs after Durham's early surge.
Stokes paid the price for an ambitious reverse sweep off Beer when he missed and was adjudged lbw for 34 falling lbw for 34, and the pressure of the spin duo of Beer and Briggs accounted for Tom Latham and Paul Collingwood cheaply as the visitors began to put a stranglehold on the innings.
After dropping Will Smith, Briggs made amends with a fine grab off his own bowling to reduce the hosts to 92 for five, before Ryan Davies was undone by a slower ball from Archer as the innings looked in danger of subsiding quickly.
Some late hitting by Stuart Poynter, who finished with 28, allowed the Jets to push their total up to 140, but that always looked below par despite an early setback for the Sharks.
The dangerous Phil Salt chipped to Stokes at mid-on in the first over before Mark Wood produced a steep bouncer to remove Luke Wright and leave the visitors 28 for two.
Any tension quickly subsided however as the eye-catching Rawlins arrived at the crease and took the attack to the Durham bowlers, crunching three boundaries to the fence early on.
He and Evans combined to put on 70 for the third wicket - surviving a scare when Rawlins was dropped by Nathan Rimmington - before Wood returned to see off the left-hander for 42.
David Wiese and Michael Burgess went cheaply but Evans upped the ante to push the Sharks over the victory line, finishing unbeaten on 63 in the penultimate over to book a finals spot for Jason Gillespie's side.
