Morgan Rogers stunned the home crowd by putting Unai Emery's side ahead in the first half but PSG swiftly turned the tide as teenager Desire Doue and Khvicha Kvaratskhelia struck back before Nuno Mendes got the third in added time to give the newly crowned Ligue 1 champions a well-deserved victory.
PSG's dominance on the ball was evident as they dictated the tempo with a blend of composed possession, technical precision, and their trademark high pressing under Luis Enrique, the coach who groomed Doue into near-stardom.
Villa, whose seven-game winning streak in all competitions came to an end, will need to show more in the return leg next week.
"By order of the Paris SG fans," a banner draped over the Auteuil Kop read - a cheeky nod to the Peaky Blinders television series, which takes place in Birmingham.
Emiliano Martinez, ever the villain in France who was greeted by a barrage of boos, whistles and expletives, made his presence felt, blocking Vitinha’s low shot and denying Ousmane Dembele, whose venomous half-volley seemed destined to rattle the net.
Two saves in quick succession, and the Villa keeper was proving his worth early on.
High up the pitch, PSG were suffocating Villa, swarming with intent. It was Villa, however, who converted first on their first clear chance.
A mistake from Mendes in midfield allowed John McGinn to pounce, nicking the ball and slipping it to Youri Tielemans. The Belgian looked up, saw the gap, and whipped a cross into the path of Rogers, who finished it off with an ice-cool tap-in.
Four minutes later, PSG levelled when Doue curled one in from the edge of the box, sending the ball sailing over the grounded Martinez and under the bar.
It was yet another superb display by the 19-year-old Doue, who scored the winning penalty in the shootout against Liverpool in the last 16.
The hosts continued to press following the break and after a superb combination in the midfield, Kvaratskhelia fired a shot that went in off the inside of the near post to make it 2-1.
Achraf Hakimi came close to adding another goal at the end of a sharp counter-attack, only for Martinez to fully stretch to tip away the ball.
PSG were denied a penalty claim and Hakimi had a goal disallowed for offside but Mendes netted two minutes into added time when he cut inside Ezri Konsa and slotted past Martinez, who left the pitch with his head down.
Barca thump Dortmund
Imperious Barcelona thumped visitors Borussia Dortmund 4-0 in their Champions League quarterfinal first leg after Robert Lewandowski netted twice against his old club to earn the Catalans a sizeable lead.
The treble-chasing Barca predictably dominated the opening stages and grabbed the lead following Raphinha's strike in the 25th minute. A string of saves from Dortmund keeper Gregor Kobel frustrated Barca for the remainder of the first half.
Barcelona emerged more determined following the break and it took them only three minutes to score the second with Raphinha assisting Lewandowski, who nodded home from close-range.
The Polish striker extended their lead in the 66th minute from just inside the box while Lamine Yamal wrapped up another demolition job by Barcelona in the 77th minute.
In yesterday's quarterfinals Arsenal stunned Real Madrid 3-0 in London, while Inter Milan beat hosts Bayern Munich 2-1.
