The visitors, appearing in the last eight of the competition for the first time in their history, took the lead in Paris before the hosts fought back, but Fernandinho's strike 18 minutes from time rescued a 2-2 draw from an action-packed contest.
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PSG quickly fought back, though, and felt that they should have had a penalty with seven minutes on the clock when Blaise Matuidi went down under the challenge of Eliaquim Mangala with only Joe Hart in front of him.
The hosts only had to wait five more minutes before they were awarded a spot kick, though, as Bacary Sagna left a leg out for Luiz to go over, and this time referee Milorad Mazic has no hesitation in pointing to the spot.
Zlatan Ibrahimovic stepped up fresh from scoring a hat-trick at the weekend, but he couldn't convert from 12 yards as Hart got down to his right to push the penalty away.
The Swedish striker had another chance moments later when he found space at the back post to nod a header towards goal, but Hart was there once again to make a more routine stop this time.
David Silva steered a header of his own wide of the target in the 21st minute, before Ibrahimovic was presented with another clear chance only to put his finish over the crossbar with only the keeper to beat.
The 34-year-old's uncharacteristic profligacy proved costly with just seven minutes of the first half remaining when Man City took a surprise lead, with Fernando and Fernandinho combining to set up Kevin De Bruyne, who lashed his finish past Kevin Trapp from inside the area.
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They were ahead for just three minutes, however, as Fernando gifted the hosts an equaliser when he collected a short goal kick from Hart and then saw an attempted pass blocked by Ibrahimovic and rebound into the unguarded net.
PSG had a chance to take the lead before half time too when Matuidi was played in down the left channel but then overhit his cross when a simple low pass into the middle would have left Edinson Cavani with a tap-in.
A second goal did arrive for the hosts shortly before the hour mark when Hart could only parry Cavani's header from a corner into a dangerous area, allowing Adrien Rabiot to follow in and stroke home the rebound from close range.
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City suddenly found themselves hanging on to keep the deficit at just one, but they were indebted to the woodwork three minutes later when Ibrahimovic's floated header came back off the crossbar and Cavani sent the rebound bouncing over.
The visitors still carried a threat on the break, though, and they were able to nick a second away goal with less than 20 minutes remaining when a loose ball fell to Fernandinho inside the box and his shot deflected off Thiago Silva and in.
PSG were unable to come up with a response in the closing stages as City comfortably saw the game out, taking two crucial away goals back to the Etihad Stadium for next Tuesday's second leg.