The Bees, who last played in the top flight in 1947, missed out on automatic promotion on the last day of the season and then lost the semi-final first leg 1-0 in Wales.
But a superb start on Wednesday (July 29) set Brentford on their way to a 3-2 aggregate success.
Ollie Watkins raced onto Mathias Jensen’s defence-splitting pass after 11 minutes and finished calmly as Swansea were punished on the counter-attack.
The hosts then led for the first time in the tie just four minutes later as Emiliano Marcondes headed in unmarked when found by Said Benrahma, who soon struck the post.
And Swansea’s hopes of a swift second-half recovery were dashed when Bryan Mbeumo added a superb third 54 seconds after the interval.
— Brentford FC (@BrentfordFC) July 29, 2020
A dismal Pontus Jansson error teed up Rhian Brewster for a lob that brought the visitors back into the match with 12 minutes to go, but Brentford battled bravely to book a Wembley date.
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