Cedric Mongongu, a former player for les Rouge et Blanc, converted from the penalty spot to give the relegation contenders a shock win over Ligue 1's second-place side
Throughout the first half the hosts impressed with impeccable organisation as action in the final third from the second-placed Ligue 1 side was minimal.
In the second half, Claudio Ranieri's men perked up somewhat - with James Rodriguez guilty of a glaring miss - but the hosts, who had claimed Paris Saint-Germain's scalp at the Parc des Sports earlier this season, were gifted a penalty late in the game when Ricardo Cavarlho handballed inside the box.
Former Monaco defender Cedric Mongongu stepped up to put les Rouge et Blanc to the sword from the spot kick, with Monaco unable to fashion a reply in the dying minutes of the match.
The loss keeps Monaco in second - well clear of third-placed Lille but 12 points behind leaders PSG - while Evian will be hoping that the hard-fought win helps to keep them afloat as they hover on the edge of the relegation zone.
Les Croix de Savoie started as they meant to go on by keeping Monaco quiet in the opening stages, with the visitors taking 10 minutes before Lucas Ocampos' deflected shot looped from 25 yards on to the top of the net.
The clash continued to work in Pascal Dupraz's men's favour. Although they did not dominate possession, they restricted the hosts' chance creation and counterattacked with menace and pace.
One of the best opportunities of the opening 45 minutes was only really a half-chance, such was Evian's effective neutralising of les Rouge et Blanc's attackers, as Daniel Wass headed down for Clarck N'Sikulu with just under half an hour gone but Monaco goalkeeper Danijel Subasic pounced to block as he shot.
Wass threatened again a few minutes later but his pot-shot from distance dribbled harmlessly wide.
A lofted ball forwards to Dimitar Berbatov as half-time lingered was met by the Bulgarian on the volley first time from 15 yards, but it skidded wide as the visitors remained frustrated by Evian's organisation.
Less than two minutes later, though, the former Manchester United forward forced a save from Jesper Hansen after weaving into the box and shooting straight at the hosts' shot-stopper.
The largely ineffective Ocampos was hauled off by Ranieri at half-time and they should have been ahead on 50 minutes.
Substitute Valere Germain crossed for Rodriguez but somehow the former Porto forward failed to convert from five yards, getting the ball stuck under his feet.
Monaco looked the better team as the second half wore on, seeking to wear out the spirited hosts, but their persistence waned in the final 20 minutes and the balance swung in Evian's favour
Nicolas Benezet, brought off the bench in the second half, drove powerfully across the 18-yard box before skimming a fierce effort just over the bar, then not long afterwards a corner flew dangerously across the face of goal as Evian pressed for an unlikely winner.
Their golden chance came with just eight minutes to go as Cedric Barbossa dummied in the area to send one Monaco defender flying then Carvalho carelessly flung his arm out in a bid to block the Evian subtitute's shot only for the referee to penalise him by giving a penalty.
Mongongou converted against his former club with consummate calm, sending Subasic the wrong way, before helping the defensive ranks hold on for all three points at the Parc des Sports.