Both the Red Bulls and Bratislava lost their opening Group F matches and with a tough-looking trip to Athletic Bilbao as their next fixture in the Europa League, Ricardo Moniz's side will be aiming to keep their impressive record against Slovakian opposition intact.
The Red Bulls have won all four of their games against teams from Slovakia without conceding a goal and in their last three home fixtures in the Europa League, they have not conceded a goal.
However, Slovan are unbeaten in their last five European away games, including a draw at the Stadio Olympico against AS Roma that saw them through the play-offs and into the group stages.
Red Bull Salzburg v Slovan Bratislava, Thursday, September 29, 21:05, Red Bull Arena, Salzburg
Elsewhere on Matchday Two, former Red Bulls head coach, Huub Stevens, who led Salzburg to the Austrian title in 2009/10 has been appointed as the new coach of FC Schalke, ahead of their clash with Maccabi Haifa.
The 57-year-old won the UEFA Cup with the German side in his first spell at the club in 1997, along with two German Cup wins in 2001 and 2002.
Stevens, who was also voted Schalke's 'coach of the century' in 1999, has signed a two-year deal with the Gelsenkirchen club and takes charge of training for the first time on Tuesday.
FC Schalke v Maccabi Haifa, Thursday, September 29, 19:00, Arena AufSchalke, Gelsenkirchen
The much travelled 28-year-old joined the Dublin outfit on 31 August this year after spells in Hungary, Moldova and Germany and made 30 appearances for Tottenham between 2002 and 2005.
The Group A clash will be Shamrock Rovers' first competitive match in England since losing their European debut 9-2 on aggregate to the Manchester United side that would be decimated by the Munich air disaster later that season.
Tottenham Hotspur v Shamrock Rovers, Thursday September 29, 21:05, White Hart Lane, London
UEFA Europa League – Matchday two fixtures (29 September)
Rubin Kazan v PAOK
Lokomotiv Moscow v Anderlecht
Metalist v AZ Alkmaar
Malmo v Austria Vienna
Sporting Braga v Club Brugge
Maribor v Birmingham City
Celtic v Udinese
Rennes v Atletico Madrid
FC Schalke v Maccabi Haifa
AEK Larnaca v Steaua Bucharest
FC Twente v Wisla Krakow
Odense BK v Fulham
AEK Athens v Sturm Graz
Tottenham Hotspur v Shamrock Rovers
FC Vorskla Poltava v Hannover
Standard Liege v Copenhagen
Legia Warsaw v Hapoel Tel Aviv
Rapid Bucharest v PSV
FC Vaslui v FC Zurich
Sporting Lisbon v Lazio
Maccabi Tel Aviv v Dynamo Kiev
Stoke City v Besiktas
FC Red Bull Salzburg v Slovan Bratislava
Athletic Bilbao v PSG