After a narrow first-leg defeat, Marseille's quest to restore parity paid dividends in the 79th minute when Faris Moumbagna headed home his first European goal for the club.
The tie ultimately finished 2-2 on aggregate after extra-time, ensuring a penalty shootout was required to decide the winner.
The hosts kept their composure to score all four of their penalties and take advantage of Angel Di Maria's miss and Antonio Silva's saved effort.
Marseille will now go on to face Liverpool's conquerors Atalanta in the semi-final, while Benfica will have to turn their focus back to domestic action.
Goalless first half
Benfica travelled to France with a slender lead after goals from Rafa Silva and Di Maria guided them to a 2-1 win in Lisbon last week.
Marseille's Iliman Ndiaye attempted to wipe out Benfica's advantage in the eighth minute, but he ultimately saw his low strike kept confidently kept out by Anatoliy Trubin.
While Benfica's primary focus was to protect their lead, they threatened to strengthen their hold on the tie when David Neres teed up Silva, who was unable to keep his effort below the crossbar.
The Europa League's all-time leading scorer Pierre-Emerick Aubameyang then thrashed an effort over Trubin's goal after being gifted possession on the edge of the box.
Marseille's patience pays off
The chances ultimately dried up until Fredrik Aursnes lifted the ball into the side netting just before the hour mark.
Despite being in the driving seat, Benfica presented Marseille with the chance to pull level when Trubin dropped the ball from a floated corner, allowing Jordan Veretout to get a shot away at goal.
Fortunately for the visitors, the Ukrainian goalkeeper was able to deflect Veretout's effort wide, ensuring Benfica's narrow advantage remained intact.
Just moments later, Trubin showcased his quick reactions to dive down to his left to thwart Geoffrey Kondogbia.
After seeing his opposite number make a sublime stop, Pau Lopez then made his own important intervention, producing two strong saves in quick succession to deny Silva and Di Maria.
Benfica were ultimately made to rue those missed chances when Moumbagna restored parity to spark scenes of jubilation inside the Stade Velodrome.
The substitute managed to squeeze his header past Trubin after meeting Aubameyang's lofted cross from the left flank.
Benfica fail to keep their nerve
Despite being pegged back in regulation time, Roger Schmidt's side went closest to winning the tie in the additional 30 minutes.
Di Maria saw his near-post header kept out by Lopez, before the Lyon goalkeeper was required to make another important stop from Arthur Cabral's 109th-minute effort.
With neither side able to find a winner, the gripping quarter-final tie went to penalties, with Di Maria firing Benfica's first spot-kick against the upright.
The following five penalties were converted before Benfica defender Antonio Silva saw his effort saved by Lopez.
Luis Henrique subsequently stepped up to dispatch the winning spot-kick and seal Marseille's place in Europa League semi-final.