The Ligue 1 side squandered a two-goal lead from the first leg and saw the tie go all the way to extra time after the hosts scored two goals in the opening 20 minutes of the second half.
Amadou Haidara's fine individual strike and a Bouna Sarr own goal ensured that momentum was with Salzburg for the additional 30 minutes, but it was veteran defender Rolando who provided the decisive moment, tucking home from a Dimitri Payet corner that was wrongly awarded 116 minutes in.
Despite losing 2-1 on the night at the Red Bull Arena, Marseille progress through to the final where they will meet Atletico Madrid, who were victorious against Arsenal elsewhere this evening.
Marseille's gameplan worked a treat in a goalless first half, blocking off all avenues to keep the game tight as they looked to protect their two-goal lead from last week's first leg.
Pele could only parry the ball back into the middle of the box, where makeshift centre-back Luiz Gustavo was well positioned to boot it clear.
That was near enough the only scare that the visitors had to survive in the opening 45 minutes, and they almost extended their lead a quarter of the way through via Morgan Sanson's first-time shot that crept wide.
Salzburg, on course to win a fifth domestic double in a row over the next week, looked the more composed in possession - as they did in the first leg - but Marseille were comfortable enough come the midway point with their advantage still intact.
The home side staged a memorable comeback to overcome Lazio in the second leg of their quarter-final tie and had netted 12 times in their seven knockout-round ties.
Inspiration was lacking at the Red Bull Arena on one of the biggest nights in Die Roten Bullen's history, though, as they failed to pose a serious threat in the final third up until their breakthrough goal.
Prior to that, Valere Germain, brought in for the injured Konstantinos Mitroglou up top in Marseille's only change from the first leg, volleyed wide from a perfectly-weighted Payet pass at the end of a swift counter.
That missed chance would prove to be a big moment in the tie, as Haidara scored a fine individual goal for the Red Bulls a few minutes later, weaving his way past four opposition men and then prodding the ball past Pele.
With momentum on their side, Andre Ramalho's belter from more than 40 yards out was again parried by Pele, and Dabbur got his connection all wrong when a cross came into the box from the right.
Salzburg had their second goal 65 minutes in following some poor Marseille defending as Adil Rami only half-cleared a cross, allowing Xaver Schlager to get a shot away which Sarr turned into his own net from a few yards out.
The flow of the game remained the same - Salzburg dominating things and all of a sudden looking far more threatening, coming close to a third soon after when substitute Hwan Hee-chan's shot was turned aside by Pele.
Marseille did manage to grab a foothold in the match as the game entered its final quarter, seeing Florian Thauvin clip the top of the crossbar with his header from what proved to be the last chance of the 90 minutes of normal time.
From cruise control to crumbling, Marseille were wayward with a couple of shots in the first half of extra time, while Dabbur failed to make the most of his side's best opening 103 minutes in.
Then came the killer moment in the tie when Rolando, unlike Dabbur before him, converted from inside the box from his side's first effort on target after being picked out from a corner, which replays show should have resulted in a goal kick.
Haidara - Salzburg's best player on the night - was dismissed late on for catching Payet with a flailing arm at the conclusion of another dramatic European night that ended with Marseille's players celebrating.
RED BULL SALZBURG: Walke; Lainer, Ramalho, Caleta-Car, Ulmer (Pongracic 96'); Haidara, Samassekou, Berisha; Schlager (Minamino 84'); Gulbrandsen (Hwang 69'), Dabbur
MARSEILLE: Pele; Sarr, Rami, Luiz Gustavo, Amavi; Lopez (Zambo 66'), Sanson (Rolando 101'); Thauvin, Payet, Ocampos; Germain (Njie 84')