A second-half strike from Andre Ayew was enough to propel Swansea to victory in the first leg, with the two sides vying for a spot in the final against either Fulham or Cardiff City.
Despite ending the season 11 points behind Brentford and just about managing to pip Nottingham Forest to the final playoff spot, Swansea produced a resolute performance at the weekend as they gained the upper hand over Brentford in the race for promotion.
Ayew fired in a thunderous volley for Steve Cooper's side 16 minutes after seeing his penalty saved, and Brentford could not find a response in the dying embers as the Swans held on for a crucial win.
The game was marred by the controversial red card brandished to Brentford's Rico Henry for a challenge on Connor Roberts, but Swansea will give no thought to the manner of their victory as they endeavour to reach the playoff final for the first time since 2011.
The Swans must now produce another strong performance of defensive resilience if they are to keep the Brentford attack at bay in midweek, but Cooper's men have now enjoyed victory in their last three outings and are yet to taste defeat on their travels since the restart.
While Swansea have enjoyed three victories from three, Brentford are in turmoil by contrast as they succumbed to their third defeat in a row at the Swansea City Stadium.
Thomas Frank's men could have secured automatic promotion to the top flight with victories over struggling Stoke City and Barnsley outfits, but Brentford crumbled at the worst time possible and were ultimately forced to settle for a playoff spot despite their otherwise outstanding season.
Failure to make the playoff final would be a disastrous outcome for a Brentford side on the brink of a top-two finish before the final day, but Frank's men have another 90 minutes to turn the tie around before they bid farewell to Griffin Park.
The Bees have plied their trade at the stadium for 116 years and there will undoubtedly be an extra motivation for Frank's men to play their hearts out on Wednesday, but there is no time for sympathies in a game with so much at stake and Swansea are travelling to Griffin Park intent on spoiling the Brentford party in the second leg.
The attacking threat posed by the Bees is certainly not to be underestimated, though, as the trio of Ollie Watkins, Said Benrahma and Bryan Mbeumo have amassed 57 league goals between them during the 2019-20 campaign.
Brentford Championship form: WWWLLL
Swansea City Championship form: WLDWWW
Brentford have successfully appealed against Henry's red card from the first-leg defeat and the left-back is available for Wednesday's second leg.
Henry has not missed a single Championship game for the Bees this term, and the 23-year-old will be expected to start once again in midweek after his three-match ban was overturned.
In the middle of the park, Emiliano Marcondes came off the bench in the first-leg defeat and has a chance of featuring from the first whistle in midweek.
As for Swansea, Cooper will likely be reluctant to make too many alterations to the side that performed valiantly in the first leg.
Brentford possible starting lineup:
Martin; Dalsgaard, Jansson, Pinnock, Henry; Marcondes, Norgaard, Dasilva; Mbeumo, Watkins, Benrahma
Swansea City possible starting lineup:
Mulder; Guehi, Hoorn, Cabango; Roberts, Grimes, Fulton, Bidwell; Gallagher; Ayew, Brewster
We say: Brentford 2-0 Swansea City
Brentford will undoubtedly be desperate to go out with a bang as they step foot onto the Griffin Park turf for one last time. The Bees spurned several opportunities in the first leg and Swansea have shown their strength in defence recently, but we expect Frank's side to end their losing streak, give Griffin Park the perfect send-off and book their spot in the playoff final.