The last time the defending champions avoided defeat for so long was during the title-winning season of 1993-94, while PSG came into this encounter without a defeat over 90 minutes in 36 matches in all competitions.
Both sides missed several chances in the first half and it remained goalless until the 75th minute when substitute Clarck N'Sikulu hit a controlled shot into the bottom corner.
Javier Pastore went close to levelling with three minutes left, but goalkeeper Jesper Hansen made the save before Modou Sougou completed a famous home win.
PSG pressed with intent in the final 10 minutes, but poor distribution coupled with Evian's determined defending ensured the hosts took all three points.
Evian coach Pascal Dupraz named one change from the weekend defeat to Bastia as Djakaridja Kone replaced Aldo Angoula, while Laurent Blanc made six alterations from PSG's 4-0 win over Lyon, with young duo Lucas Digne and Adrien Rabiot returning.
The home side had a great chance to take the lead in the ninth minute as Sougou released Brice Dja Djedje into the area on the counterattack, but the full-back blazed over from an acute angle.
Less than two minutes later, Edinson Cavani should have scored as he got on the end of Zlatan Ibrahimovic's chipped cross, but the unmarked Uruguayan headed over.
Ibrahimovic was lucky to stay out of trouble in the 30th minute as his studs collided with the head of Jonathan Mensah and he was in the thick of the action a few moments later, but Jeremy Menez failed to bundle his low cross over the line.
The last chance of the half also fell to Menez, but after getting on to Cavani's pin-point delivery, the France international volleyed just over crossbar.
For the 20 minutes that followed half-time, Blanc's men were forced to contend with set-pieces, yet they were generally ineffective as Hansen was given few saves to make.
Salvatore Sirigu, Hansen's opposite number, was not so fortunate at the other end, however.
Sougou chased down a long ball and a ricochet saw it drop to the edge of the area for N'Sikulu, who caressed a shot into the bottom corner of the net four minutes after coming on.
Pastore should have equalised in the 87th minute as he headed Ibrahimovic's cross at Hansen and Evian went down the other end to double their lead as Sougou skipped past a challenge and swept a shot past Sirigu.
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