Ollie Watkins, Emiliano Marcondes, and Bryan Mbeumo scored to give Brentford breathing space after Sunday's 1-0 first-leg defeat in south Wales. Swansea ensured a nervy finish when Rhian Brewster intelligently lifted the ball over David Raya in the 78th minute, but Brentford held onto their one-goal lead over the two meetings.
The playoff semifinal win occurred in the Bees' last-ever match at Griffin Park, their home since 1904. They are now one match away from celebrating their stadium move by playing top-tier football for the first time since 1947.
Brentford leveled the tie on aggregate when goalkeeper Raya quickly released a ball to Mathias Jensen, who then threaded a pass through a small fissure in the Swansea defense. Watkins, who finished behind Fulham's Aleksandar Mitrovic in the Championship's top-scorer race, neatly tucked the ball under Erwin Mulder.
The fluidity of Thomas Frank's formation was evident in Brentford's second. Watkins and Said Benrahma both dropped deep to create the move, and the latter's delivery was met by Marcondes' deft header into the bottom corner.
The hosts plumped up a two-goal cushion over the two legs when Rico Henry's cross was superbly volleyed home by Mbeumo shortly after the break. But, as some players on the Brentford bench exchanged high-fives, Pontus Jansson's strange attempt to clear danger with a backheel was preyed upon by Liverpool loanee Brewster.
Brentford saw out the win, though, and will now have a second chance at securing Premier League football after narrowly missing out on automatic promotion behind Leeds United and West Bromwich Albion.