A surprising 3-0 loss in Amsterdam has left Ajax chasing the game heading to Austria for Thursday's second match between the teams.
Salzburg reached their only major European final 20 years ago, when in the days of two-legged UEFA Cup finals they were beaten 1-0 both home and away by Inter Milan. They were also known as Austria Salzburg in those days.
Energy drink manufacturer Red Bull bought Salzburg in 2005, sinking in major investment and securing a controversial rebranding as Red Bull Salzburg that is not recognised by UEFA. Since then, the club have been building towards weeks such as this, when they compete with the biggest clubs in Europe.
As sporting director Ralf Rangnick said on Wednesday: "Until now, in the Red Bull era we haven't succeeded in getting to the last 16. That would be a great success."
Coach Roger Schmidt is determined to keep his players' motivation high for a tie it would be easy to assume is effectively already over.
"We have created for ourselves a very good starting point," Schmidt said. "We can gain our reward for the development we have achieved in the last year and a half.
"Ajax will certainly show a reaction, and we must be ready for that. I expect there will be a real battle in our stadium. We must be as focused as we were in Amsterdam. Then I am convinced that we will win this match and earn the right to progress."
Salzburg have not lost at home since last May, but Schmidt said: "That doesn't mean that we think we are unbeatable. It's not like we have discovered something new. At the same team, the team is convinced that the way we play works."
Four-time European club champions Ajax are not the only high-profile team in danger of an early exit in the group stages.
Lazio trail Bulgarian side Ludogorets 1-0 ahead of their game in Sofia, and have travelled without injured defender Andre Dias, while Lyon will look to make a breakthrough at home against Ukrainian side Chornomorets after a goalless first leg.
Fiorentina will look to finish off Esbjerg, armed with a 3-1 lead from last week's match in Denmark, and Tottenham trail 1-0 heading into their White Hart Lane tussle with Dnipro.
Juventus are the bookmakers' tournament favourites, and Antonio Conte's team carry a 2-0 lead to Turkey for their second match against Trabzonspor.
Valencia and Dynamo Kiev had to move their first leg at short notice from the Ukrainian capital to Cyprus, due to political unrest and bloodshed on the streets, and the Spanish side won 2-0 in Nicosia, making them firm favourites to reach the last 16.
Benfica lead PAOK Salonika 1-0 and are at home in the second leg. AZ Alkmaar are in precisely the same advantageous position in their tie with Liberec.
Each other head-to-head is level at the halfway stage, with the first-leg matches between Napoli and Swansea, Genk and Anzhi Makhachkala, and Basle and Maccabi Tel Aviv having all finished goalless.
Shakhtar Donetsk and Plzen played out a 1-1 draw, as did Rubin Kazan and Real Betis, while Eintracht Frankfurt and Porto finished 2-2, the same scoreline that Sevilla and Maribor will resume at on Thursday.