Bairstow struck three sixes and two fours in his 68 not out that provided the backbone to his side’s total of 172 for six.
Things looked bleak for Yorkshire when they slipped to 36 for three, only for David Miller (47) to help put on a fourth-wicket stand worth 82 that turned the tide against the Sharks.
The White Rose county, who won the toss and opted to bat first, saw their top three all fall to the wily medium pace of Scott Styris, who combined with spinner Michael Yardy in taking the new ball.
Andrew Gale, Joe Root were both dismissed by the New Zealander for 11 to ill-advised strokes while Phil Jaques was bowled having managed just two from nine deliveries.
However Miller - who had flown in from South Africa A’s tour of Ireland - and Bairstow gradually rebuilt the Yorkshire innings to lay the platform for a second-half onslaught.
Miller was caught just short of his half-century off the bowling of Chris Nash, but Bairstow, fresh off two half-centuries in the third Test against South Africa at Lord’s, helped blitz 111 runs from the final 60 deliveries.
None of Sussex’s big guns were able to get going in the same way, their cause not helped by the early departures of Luke Wright (three) and Matt Prior, who was dismissed by England team-mate Tim Bresnan for two.
It left Chris Nash to fight a lone hand, the opener carrying his bat through the 20 overs to make an unbeaten 80 from 58 deliveries.
He struck eight fours and two sixes, both by using the ramp shot, sending the ball over the rope at fine leg, but received no real support.
Murray Goodwin was the only other Sussex batsman to reach double figures, the former Zimbabwe international making 15 before holing out to long-on off Richard Pyrah (2-30).
Bresnan picked up 2-22 as the Sharks finished well short on 136 for eight and it was Yorkshire who progressed to the final against Hampshire Royals, who beat Somerset in the day’s second semi-final.