Quickfire goals from Chancel Mbemba and Jordan Veretout in the first-half left Albion facing a damaging defeat but the visitors were much-improved after the break.
Pascal Gross – who was making his return from injury – got one back on the 54th minute, before Joao Pedro scored his third goal of the European campaign with his third penalty two minutes before stoppage-time.
Albion remain bottom of Group B after two games but are just one-point behind second-placed Marseille, and three behind Athens, who drew 1-1 against Ajax.
The Seagulls looked sluggish early on, seemingly still suffering from the effects of the 6-1 defeat at Aston Villa and dealing with an unfamiliar intense atmosphere in France.
The defenders were too static as former Newcastle defender Mbemba opened the scoring after 19 minutes. The hosts added a second just a minute later after a huge mistake by skipper Lewis Dunk was punished by Veretout. Jason Steele could have done more to keep the ball out.
Brighton responded well and they thought they had a penalty after the referee was told to check for a handball. He appeared to point to the spot after watching several replays but no penalty was forthcoming – much to the confusion of fans in the stadium and those watching at home.
The visitors kept up the pressure and should have scored before half-time.
They continued where they left off after the break and got the goal they deserved. It was the returning Gross who found the net from Kaoru Mitoma's pass after great work by Tariq Lamptey.
Marseille had lost the momentum and control of the game and it seemed a matter of time before Brighton would find an equaliser.
They had to wait until the 88th minute when Pedro kept his nerve once again to send the keeper the wrong way from the spot.
Scroll down and click through to see how we rated Roberto De Zerbi’s players:
1. Marseille 2-2 Brighton
Brighton mounted a superb second-half comeback at Marseille to earn their first ever Europa League point Photo: Mike Hewitt/Getty Images
2. Jason Steele - 6
Tried to bait the press by regularly keeping hold of the ball for an age in the first half. Marseille didn't fall for it and Albion were struggling to start attacks. Couldn't have done much to stop Mbemba's strike but really should have done better with Veretout's weaker effort. Excellent save from long range effort after Brighton gave Amine Harit too much space. More comfortable in the second half. Kept hold of a late cross well. Photo: Mike Hewitt/Getty Images
3. Joel Veltman - 6
Struggled, like most of his teammates, in the first 45 minutes. Lost ball carelessly. Nice through ball to Welbeck should have resulted in a goal before the break. Settled down defensively and in possession as Albion looked for a way back. Strong challenge on Correa. Booked in second-half Photo: NICOLAS TUCAT/AFP via Getty Images
4. Jan Paul van Hecke - 7
Good, strong defending on more than one occasion. Seemingly adjudged to have made a foul before the referee decided against giving Brighton a penalty after checking the monitor. Picked up some attacking positions. Powerful header heading in but hit Mitoma in the face. Photo: NICOLAS TUCAT/AFP via Getty Images