While the winners will advance to the playoffs, the side beaten at Stade de Geneve must face Chelsea in the Conference League qualifiers.
Match preview
Having reached the Europa League's group stage for the first time last season, Servette are aiming to qualify for the same competition again, following last term's third-placed finish in the Swiss Super League.
Les Grenats held firm to keep a clean sheet in Braga last week, despite seeing very little of the ball, and remain just one game away from the playoffs.
Though they started the new league campaign with three straight wins - over Luzern, reigning champions Young Boys and Yverdon Sport - since returning to continental competition, Servette seem to have taken their eye off the ball domestically.
Thomas Haberli's side not only suffered a setback when losing 3-1 to Lugano just before the first leg, but Sunday's Super League encounter at home to Basel certainly did not go to script.
After trailing by a goal at half time, Servette simply crumbled after the break, and a humbling 6-0 defeat could crush their confidence ahead of Thursday's big game.
Meanwhile, Braga began their new Primeira Liga season at home to Estrela last weekend, when Amine El Ouazzani's second-half strike was not quite enough to secure success on the opening matchday.
Therefore, two disappointing home draws followed a 7-0 aggregate thrashing of Maccabi Petah Tikva in the second round of Europa League qualifying, bringing harsh consequences for head coach Daniel Sousa.
A former analyst with Chelsea, Sousa only replaced previous boss Artur Jorge in May, but he was sensationally sacked immediately after Sunday's league fixture.
Without a permanent manager in place, Braga's squad must now turn their focus to avoiding a third-round Europa League exit, as they suffered to Qarabag this time last year.
Including qualifiers, Os Guerreiros are competing in Europe for an eighth consecutive season - and memorably made the final back in 2011 - so they will hope to use such experience to their advantage in Switzerland.
Should they see their way past Servette, only a playoff against either Rapid Vienna or Trabzonspor would then separate them from the Europa League's new-look group stage.
Servette Europa League form:
D
Servette form (all competitions):
W
W
W
L
D
L
Braga Europa League form:
W
W
D
Braga form (all competitions):
W
D
W
W
D
D
Team News
Thomas Haberli should have an almost full squad to choose from on Thursday evening, but he will have to make at least one change to Servette's back four.
Steve Rouiller sustained an injury during the first leg, and - after then being ruled out of league action by suspension anyway - the experienced centre-back is set to be sidelined again.
On-loan striker Victory Beniangba is also unavailable, so French forward Enzo Crivelli will bear most of the goalscoring responsibility up front; however, the latter has found the net just five times in 38 previous UEFA competition appearances.
Braga's lineup could change significantly following Daniel Sousa's removal, so players such as Bruma - who was dropped at the weekend - will hope to regain their place in the starting lineup.
Rodrigo Zalazar and veteran midfielder Joao Moutinho combined to tee up Amine El Ouazzani's goal against Estrela, and all three should be involved at Stade de Geneve.
It remains to be seen whether a managerial change will affect the futures of Andre Horta and Simon Banza, both of whom were expected to leave the Quarry this summer.
Servette possible starting lineup:
Frick; Tsunemoto, Baron, Severin, Mazikou; Ondoua, Cognat; Stevanovic, Antunes, Kutesa; Crivelli
Braga possible starting lineup:
Matheus; Gomez, Arrey-Mbi, Niakate, Marin; Zalazar, Moutinho, R. Horta; Roger, El Ouazzani, Bruma