The Austrian Bundesliga leaders came into the game boasting a 10-match winning streak in Europe this term but failed to seize the initiative in the last 16 first leg tie at St Jakob-Park.
The competition's leading scorers were unable to break down a stern Basel defence as the Swiss champions denied Roger Schmidt's men a 15th consecutive triumph in all competitions.
Goalkeeper Yann Sommer, who agreed a deal to join Borussia Monchengladbach in midweek, was called into action early on when he tipped Stefan Ilsanker's glancing header round the post.
Matias Delgado should then have done better when he ballooned a strike over following a quick break, while at the other end Dusan Svento again gave Sommer something to think about with a curling effort from inside the area.
As the visitors began to get on top in the game, Sadio Mane felt that he should have been awarded a penalty after turning past Marek Suchy –although referee Ovidiu Hategan disagreed and booked the Senagal midfielder for simulation.
Basel almost moved into the lead shortly after the half-hour mark when Giovanni Sio diverted Philipp Degen's delivery over the bar after a speedy counter-attack.
And Valentin Stocker threatened on the stroke of half-time when fired a shot straight at Peter Gulacsi from close range.
After a quiet first half, Salzburg captain Jonathan Soriano eventually sprung into action shortly after the break, hitting two efforts from distance - one wide and the other comfortably saved - as he sought to maintain his status as the Europa League's leading scorer.
However, in the absence of Alan, the visitors struggled to showcase the attacking qualities that saw them score 36 goals in their previous eight games.
Robert Zulj was unable to convert Kevin Kampl's cross late on as Schmidt's side failed to find the net for the first time since December 2012.
