Salzburg last tasted defeat against Rapid Vienna on November 24 and while they remain unbeaten in the competition, they were unable to take an advantage back to Austria for the second leg of the tie.
Basel started strongly with a good effort from Matias Delgado flashing wide after the Argentinian was the last man in a pacy break upfield, but Kevin Kampl and Sadio Mane threatened in the wide channels for Salzburg several times in the first half.
Basel finished the first period the strongest, though, and had the best scoring change of the half when Giovanni Sio headed over from close range however the deadlock remained intact at the break.
Stefan Ilsanker had the first chance of the match for the runaway Austrian Bundesliga leaders when the Salzburg midfielder forced a save from Yann Sommer in the third minute from a free-kick.
Delgado then fired wide before Salzburg wrestled back the initiative and Mane headed straight at Sommer from a Kampl cross.
Kampl, who was starting to assert himself on the game, forced a fine save from Sommer at his near post as the visitors stretched the home side and began to dominate in midfield.
Sio missed the target as he headed over in the 33rd minute as both sides failed to find the breakthrough before the half-time whistle.
After the interval, chances were few and far between, with Jonatan Soriano's long-range attempt in the 55th minute the best of a scant showing early in the second period.
Sommer made the save from 25 yards and the game settled down, with the next chance a wasted one when Gaston Sauro stopped Mane's cut-back from finding Soriano in the area with a quarter of the game left to play.
Salzburg substitute Valon Berisha had a good effort saved by Sommer after he caught the ball well on the edge of the area in the 86th minute in what was the last throw of the dice, with neither side able to take an advantage into the second leg.