After Yorkshire posted 177 for seven, Afghanistan’s spin superstar came in at 135 for four after 16.3 overs, with 43 required.
Khan mixed power with invention, hitting three fours and two sixes, before Chris Jordan hit the winning runs - the game sealed by five wickets with two balls remaining after Luke Wright’s excellent 54 off 39 at the top of the order.
Yorkshire were indebted to 55 apiece for Gary Ballance and opener Tom Kohler-Cadmore on a true pitch with short boundaries.
After the Vikings slipped to 33 for three after five overs, left-handed Ballance found fluency quickly as Kohler-Cadmore struggled for rhythm.
After getting Harry Brook lbw sweeping for one, leg-spinner Khan (one for 25) was played with comfort.
Ballance pulled him over midwicket for six to reach a 34-ball fifty.
Alongside Brook’s departure, Yorkshire lost Adam Lyth and captain David Willey cheaply to Archie Lenham and Tymal Mills.
But, as Ballance led the recovery and paved the way for Kohler-Cadmore to find late fluency, Sussex’s fielding was sloppy. It later transpired that both sides were off colour.
Mills finished with three for 39. Kohler-Cadmore, meanwhile, reached his fifty off 47 balls.
Wright came out with serious intent in a bid to put a huge dent in the chase. And it worked, with the Sharks reaching 53 without loss after six overs.
He pulled Matthew Fisher for a vicious flat six over midwicket before being dropped on 31 off Matthew Waite - a skied catch to wicketkeeper Harry Duke with the last ball of the powerplay.
Jordan Thompson ended a 72-run opening stand in his first over - the ninth - when Phil Salt found long-on for 27.
Wright reached his fifty off 32 balls early in the 11th before Duke atoned for his earlier error with a fine one-handed catch to help Thompson get rid of Ravi Bopara - 91 for two.
Adil Rashid bowled a sweeping Wright early in the 13th over, leaving the score at 111 for three with 67 still needed.
That target later became 56 off five at 122 for three with David Wiese and Delray Rawlins together.
Fisher bowled Rawlins for 27, leaving Sussex at 135 for four and needing 43 off 21.
But Khan crashed sixes off Fisher and Thompson, one brilliantly over long-on, and took Willey for three fours in a telling penultimate over to leave only six needed off the last.
Unfortunately, he will not be available for next month’s Edgbaston showpiece.
He said after he collected the MoM award: "I just wanted to back up my skills and I thank the coaching staff for sending me in a bit earlier. Sometimes even I don't know where I'm hitting the ball but I always have in mind just to hit it hard and play according to the ball. I'm so happy to help Sussex to Finals Day and I wish them all the best.
“I’m so happy to see the team in the finals twice since I’ve been in the team (the other in 2018). But it’s a shame I won’t be available for them at Finals Day. Every player would love to be there.”