The Italian boss suffered his maiden loss en route to exiting the competition as Remi Garde's men booked a ticket into the semi-finals after a pulsating tie
Nene opened the scoring for the hosts with a penalty in the 19th minute following Samuel Umtiti's handball. The visitors restored parity with a fine free-kick from Kim Kallstrom before taking the lead through Lisandro Lopez's calm finish. Bafetimbi Gomis made the game safe from the spot in injury time.
Les Parisiens had the chances, and failed to take any of them, being denied by an inspired Hugo Lloris. Javier Pastore, on as a second half substitute seemed to revitalise the team, though he, along with Blaise Matuidi, Jeremy Menez and Kevin Gameiro would be guilty of wasteful finishing.
Ancelotti rang the changes for the cup tie, with Nicholas Douchez replacing Salvatore Sirigu in goal and the likes of Sylvain Armand and Diego Lugano were given a run-out ahead of of Mamadou Sakho and Alex. Lyon meanwhile, elected to start Samuel Umtiti in place of Bakary Kone as they remained largely unchanged.
Despite Remi Garde's men enjoying the best of possession early on, it would be the Ligue 1 leaders who created the first gilt-edged chance of the counter. Nene, impressive in recent weeks, attempted a lovely ball over the defence in towards Gameiro, though Lloris managed to see out the ball to safety.
Gameiro, who has lost his place recently to Guillaume Hoarau, would also go close for the second time before the Parisiens would benefit from a fortuitous call.
Sylvain Armand, making his 350th appearance for the capital club and awarded the captaincy for the occasion, fired towards goal, hitting the arm of Umtiti, and the referee had no hesitation in awarding the penalty. Nene stepped up to dispatch the spot-kick coolly to put les Parisiens ahead.
The lead, however, only lasted for all of six minutes as les Gones responded in spectacular fashion. Kallstrom curled a free-kick from 25 yards over the wall and into the back of the net leaving a bemused Douchez to ponder his positioning, as Garde's men drew level.
Gameiro would again be the victim of his own profligacy as he spurned two great chances, most notably from Nene's weighted pass into Lloris' arms, and this time he would be punished. Lyon countered and Kallstrom's fine cross bobbled horribly in front of Douchez, leaving Lisandro to tap into the net for 2-1.
Ancelotti attempted to reverse his side's decline with the introduction of Javier Pastore at half-time, and the the Argentine international's impact and influence told almost immediately.
Pastore opened up the les Gones rearguard with a series of through balls, and almost reaped his rewards early on as Christophe Jallet brought a fine save from Lloris with an exquisite shot.
Moments later, Lloris would be forced to action again, this time pulling off two world-class saves. Jeremy Menez, who had been impressive all evening dribbled past two defenders and fired a low shot goalwards, only to be thwarted by the goalkeeper.
For all of PSG's attacking endeavours, Remi Garde's men really should've sealed the game midway through the second half. Gomis did fantastically well to evade the offside line and selflessly squared the ball for Lisandro, only for the striker to inexplicably shoot over the bar as the Parc des Princes breathed a sigh of relief.
Remi Garde elected to defend the lead late on with the introduction of Mohamadou Dabo and Bakary Kone, which went some way into nullifying a heated PSG attack. Hoarau went close from a header, though Jallet would later be penalised for a rash challenge as Gomis made it 3-1 from the spot in the 91st minute.
Lyon now progress to the semi-finals along with amateurs US Quevilly and Grazelec Ajaccio as well as Ligue 1 side Stade Rennes. PSG meanwhile, turn their attention to the only trophy available to them, a tricky league tie against Bordeaux on Sunday.