The second goal came somewhat against the run of play, as the visitors gave a good account of themselves and squandered decent opportunities at 1-0 and 2-0, offering enough to suggest that this tie is not over just yet.
Salzburg, the only remaining side in the competition yet to lift a major UEFA trophy, took some time to get going in the sold-out Velodrome and were behind 15 minutes in.
Dimitri Payet, now directly involved in eight knockout-round goals after tonight, sent in a perfect set-piece delivery for Thauvin to guide past Alexander Walke, although the final touch came off his hand.
With momentum on their side and a vociferous home backing behind them, the Ligue 1 outfit went in search of a second and nearly got it when Morgan Sanson blasted a couple of yards wide.
After around half an hour momentum started to shift slightly, however, and Salzburg - who took four points off their opponents in the group stage - were slowly enjoying more of the ball in advanced positions.
Stefan Lainer's shot from 25 yards gave Yohann Pele a little something to think about down low from their first and only first-half effort on target, moments before Thauvin's curler was collected by Walke at the other end.
After a bright start to the second period Die Roten Bullen's best opening fell the way of Hannes Wolf, who was denied by Pele when bursting through on goal.
Rudi Garcia then made a couple of changes, including the introduction of Njie in what proved to be an inspired move - the former Tottenham Hotspur man being responsible for the tie's second goal.
Payet laid the ball into Njie's path following a swift counter and the substitute forward kept his composure to slot it past Walke.
Leading scorer Munas Dabbur wasted half a chance for Salzburg soon after as the 11-time Austrian champions chased an away goal, before Fredrik Gulbrandsen went closer with his strike against the post from a close-range chance.
That would prove to be it, leaving Salzburg - beaten for just a third time in 16 away outings - with it all to do in the return fixture next week.
MARSEILLE (4-2-3-1): Pele; Amavi, Gustavo, Rami, Sarr; Sanson, Lopez (Njie 60'); Ocampos (Andre-Frank 52'), Payet, Thauvin (Germain 81'); Mitroglou
RB SALZBURG (4-4-2): Walke; Ulmer, Caleta-Car, Ramalho, Lainer; Berisha, Samassekou, Wolf (Schlager 68'), Haidara (Yabo 81'); Dabbur, Hwang (Gulbrandsen 60')