The Czech league leaders, 1-0 down from the first leg in France, appeared down and out when Marseille went 2-1 up on the night but stormed back.
They scored three second-half goals, securing the aggregate victory with a stoppage time header from substitute Tomas Sedlacek.
Schalke 04, who lifted the trophy in 1997, also bowed out as French side AS Nancy overturned a 1-0 first-leg defeat to win 3-1 at home.
Holders Sevilla had few problems seeing off Greek side Atromitos as they ran out 4-0 winners at home to progress 6-1 on aggregate. Former winners Parma, Ajax Amsterdam, Feyenoord and Tottenham Hotspur also came through unscathed.
Marseille, twice beaten UEFA Cup finalists, seemed in control of their tie thanks to goals from Toifilou Maoulida and Taye Taiwo either side of a Lubos Pecka strike.
It left Mlada, who lost in the third qualifying round of the Champions League to Galatasaray, needing to score three times.
Substitute Radim Holub gave Mlada hope four minutes after coming on early in the second half and his second eight minutes from time set up a frantic finale, capped by Sedlacek's winner.
COLLECTIVE FAILURE
"It was a collective failure. It should have been a simple match," Marseille chairman Pape Diouf told the club's Web site.
"We took the lead early, we even led for a second time in the match.
"This is a day which will serve as a lesson for everybody. The players have to tell themselves you do not win a match without showing some humility."
Two goals in a seven-minute spell midway through the first half from Brazilian defender Andre Luiz and Uruguayan striker Gaston Curbelo set French Cup holders Nancy on their way to victory over Schalke, who have made a flying
Issiar Dia made it 3-0 before Marcelo Bordon got one back but Schalke's woes were compounded by striker Gerald Asamoah breaking his left leg.
Despite Marseille's exit it was an otherwise good night for French sides with Racing Lens, Auxerre and Paris St Germain going through.
Juande Ramos's Sevilla dominated Atromitos and within three minutes were ahead when visiting defender Vasilios Apostolopoulos put into his own net.
Seven minutes later another own goal from midfielder Dimitrios Ioannoy effectively ended the game as a contest, and in the 28th minute Sevilla's Brazilian striker Luis Fabiano pounced to make it 3-0.
Five minutes from time home striker Kepa added a fourth with an individual effort.
Twice winners Parma qualified when a goal by 18-year-old striker Daniele Paponi gave them a 1-0 win over Russian side Rubin Kazan to go through 2-0 on aggregate.
AJAX CRUISE
Ajax cruised to a 4-0 win over Norway's IK Start, completing a 9-2 aggregate rout, with Markus Rosenberg netting twice. Arch rivals Feyenoord were held 0-0 at home by Lokomotiv Sofia but went through on away goals.
Spurs have endured a poor start to the Premier League season with goals in short supply for Martin Jol's side. Ireland's Robbie Keane gave their long-suffering fans some cheer with the only goal at White Hart Lane to seal a 2-0 aggregate success over Slavia Prague.
Hapoel Tel Aviv marked the return of international competition in Israel with a 3-1 win (4-1 aggregate) over Chornomorets Odessa in front of 15,000 fans at the Bloomfield Stadium.
UEFA imposed a ban last month due to the war in Lebanon between Israel and Hizbollah Guerrillas. It forced all Israeli home fixtures under UEFA's jurisdiction to be played at other venues in European countries.
The draw for the group stage takes place on Tuesday.
