Daouda Coulibaly scored the only goal, and his second of the African campaign, after 54 minutes of the top-of-the-table Group D clash.
Victory lifted Stade to 11 points after matchday five. Esperance and Petro Luanda of Angola have six points each ahead of their meeting next Sunday, and Simba of Tanzania two.
Stade have been the surprise package of the premier African club competition this season after 19 previous failed attempts to reach the group stage.
Two Cameroonians have played significant roles in a qualifying and group campaign that has produced six victories and three draws.
Mauril Njoya coaches the 'Whites' and five-goal Taddeus Nkeng is the joint-leading scorer in the Champions League.
Stade are the third club to reach the quarter-finals after Egyptian challengers Al Ahly and title-holders Pyramids. The trio are also the only clubs still boasting unbeaten records.
Pyramids, winners of the competition last season in only their second appearance, came from behind against Rivers United to win 4-1 in Nigerian city Uyo.
Rivers led at half-time thanks to a Stephen Manyo goal, but once Mostafa Fathy levelled on 52 minutes, the defending champions took control of the Group A match.
Marwan Hamdy converted a 77th-minute penalty to put Pyramids ahead and late goals from substitutes Odeh Fakhoury and Nasser Maher completed the rout.
Pyramids have a six-point lead in the section with one round remaining. Renaissance Berkane of Morocco and Power Dynamos of Zambia have seven points each in the race to progress as runners-up.
Saint-Eloi Lupopo from the Democratic Republic of Congo and Mamelodi Sundowns of South Africa drew 1-1 in Lubumbashi to leave all four Group C clubs still in contention.
Enoch Molia tapped in a low cross to give the hosts a 19th-minute lead and Jayden Adams levelled 10 minutes into the second half by heading past goalkeeper Esdras Kabamba after a corner.
Al Hilal of Sudan top the table with eight points, Mouloudia Alger of Algeria have seven, 2025 Champions League runners-up Sundowns six and Lupopo five.
Sundowns, who reached the knockout stage in nine of the last 10 editions, were expected to dominate the mini-league, but are winless in four matches.