The Tongan prop scored two tries as Brett Hodgson’s side, full of character and grit, produced an excellent defensive display in the rain at Emerald Headingley.
There had been fears Hull would be out-muscled and over-run given they were without four front-rows against a Wigan side who had won all six games this year.
They were also missing the suspended full-back Jake Connor and saw young prop Jack Brown sin-binned in the first half but it mattered not as the Black and Whites dug deep to deliver a quality performance.
It was the perfect response after Wigan had ended Hull’s own unbeaten record nine days previously with a 16-14 defeat, a game which made continued headlines after Warriors prop Tony Clubb received an eight-game ban for racially abusing Andre Savelio.
Adrian Lam’s side were unusually error-ridden here, their sloppy display perhaps summed up by Zak Hardaker.
The England full-back has been outstanding this term yet twice kicked restarts out on the full, struck an upright with a simple penalty from in front of the posts and also spilled one downfield kick with no one near him.
Hull, in contrast, had far more control and - with Danny Houghton, Satae, Manu Ma’u and Mahe Fonua all putting in towering efforts - were deserved winners.
Having pulled 16-4 clear with Satae’s second try in the 65th minute - after Bevan French, like Hardaker, had hopelessly fumbled a harmless kick - Hodgson’s side were almost home.
Wigan had a glimmer of hope when fit-again Dom Manfredi scored two minutes from time, Harry Smith converting.
However, as they hunted a further try after the hooter had sounded, Willie Isa fumbled when space had been created and Hull full-back Adam Swift raced 70m to the delight of his team-mates.
Hull led 8-4 at the break having finished the half down to 12 men after Brown was yellow carded for a cannonball tackle on Joe Shorrocks.
That caused some consternation for Hodgson’s side who had seen their own player Josh Griffin need treatment earlier after a very similar challenge to the legs by Sam Powell, the Wigan hooker who stayed on the field.
The game was already full of niggle which was not surprising after the controversial events of their last meeting.
Here, though, both sides were into each other from the off, Griffin and John Bateman flaring up after the Hull centre’s poor defensive read saw Bibby score early on.
Powell then had words with Marc Sneyd after hitting the Hull scrum-half late following a downfield kick and every time Wigan made an error - which was often - there was plenty of close-up vocals from their opponents celebrating the error.
Rarely have Warriors made so many handling mistakes in recent times. Prop Liam Byrne made two in the opening 13 minutes and then compounded his second by failing to deal with Satae as he showed neat footwork to power over for his first try.
Sneyd improved and added a penalty soon after before their defence showed their steel, holding up Liam Farrell over the goalline.
Farrel was high on Griffin in the 53rd minute, which saw the Hull centre need to go off for an HIA, and the Wiganer’s ill-discipline continued as he shoved Josh Reynolds off the ball as the Australian chased a kick.
Sneyd missed the penalty but when Morgan Smithies hit Reynolds late after his own kick there was no mistake.
Hull’s defence was swarming at times and, though Bateman got Manfredi away from deep as they escaped their own half at last, the cover was there.
It generally always was: Hull, who defeated Wigan in the 2017 final, are just 80 minutes away from Wembley again.
Hull FC: Swift; Fonua, Tuimavave, Griffin, Scott; Reynolds, Sneyd; Sao, Houghton, Satae, Savelio, Ma’u, Lane. Substitues: Johnstone, Cator, Brown, Wynne.
Wigan Warriors: Hardaker; Bibby, Isa, Farrell, French; Smith, Hastings; Singleton, Powell, Byrne, Bateman, Smithies, Partington. Substitutes: Manfredi, Bullock, Harvard, Shorrocks.
Referee: Robert Hicks (Oldham)
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