Marseille dominated the majority of the game and weathered a short 20-minute spell where the visitors came mightily close to equalising.
However, Salzburg will feel aggrieved after being denied a certain penalty whilst being one goal behind.
Although there is an uphill task at hand, Salzburg are far from out of the tie and should take inspiration from their quarter-final second leg performance.
Early goal to settle the nerves
The home side only took 15 minutes to open the scoring when Thauvin headed home from close range after a superb free-kick from Dimitri Payet.
Goalkeeper Alexander Walke was a spectator as Payet's cross looped over his head giving Thauvin a simple header on goal.
Although it seemed a simple header, the ball appeared the hit Thauvin's arm before crossing the line.
However, Marco Rose's men had their appeal for handball ignored by Scottish referee William Collum.
The goal increased the Frenchman's tally to 23 goals in all competitions.
N'Jie seals the deal
Only two minutes after being introduced as a substitute, N'Jie doubled Marseille's lead.
The Cameroon international latched onto a pass from Payet and calmly slotted beyond Walke.
The ex-Tottenham Hotspur centre forward did not impress in his time in London but certainly provided an instant impact after coming on.
The goal came at a time when the Austrian opposition were growing into the game as they pressed for an equaliser - a timely goal.
Neither team managed to construct any clear chances on goal after Thauvin's goal, with all shots coming from outside the box.
Marseille control first 45
Yohann Pelé remained comfortable between the sticks with Salzburg only managing one shot on target.
Stefan Lainer shifted the ball onto his left foot but his effort from outside the area was easily smothered by Pelé.
Les Olympiens remained in control for the rest of the first half with their main threat coming down the right side through Payet.
Andreas Ulmer had a torrid first 45 minutes with Payet and Thauvin taking turns to exploit the visitors' left-back.
Rose will have been glad to get his men in the changing room at half-time, Die Roten Bullen were unable to get a grip on the game and were in danger of losing more ground on the tie.
Salzburg denied a certain penalty
The visitors sprung into action in the early stages of the second-half, after being denied a certain penalty on the 50th minute after Lainer was brought down.
After being denied the penalty, Hannes Wolf was miraculously denied by a strong palm away from Pelé - tipping the shot from inside the box over for a corner.
Momentum was certainly with the visitors but their efforts were crushed when N'Jie entered the pitch on the hour mark.
Despite conceding for the second time on the night, the Salzburg players did not allow their heads to drop.
Substitute Fredrik Gulbrandsen struck the left post with a driven shot, a whisker away from putting his side back in the tie.