PSG, playing in their fourth straight quarter-final in the competition, fell behind when Kevin De Bruyne opened the scoring in the 38th minute, but Zlatan Ibrahimovic capitalised on a City blunder to level, having earlier missed a penalty.
The home side, who had exited at this stage for the last three seasons, then took the lead through Adrien Rabiot just before the hour but Fernandinho made it 2-2 after benefiting from a PSG mistake.
City, who are playing in the quarter-finals for the first time, will host PSG at the Etihad stadium next Tuesday, where boss Manuel Pellegrini is hoping for more of the same.
“We have to keep that mentality for the second leg,” he said.
His PSG counterpart Laurent Blanc, however, was left to rue a disappointing display.
“It`s not a good result, we made too many technical mistakes,” the former France centre back said.
Both teams were without key midfielders as City`s Yaya Toure was ruled out with a knee injury and PSG`s Marco Verratti was sidelined with a groin problem.
PSG, crowned Ligue 1 champions last month, were boosted by the return of Serge Aurier, who was handed his first start since insulting coach Laurent Blanc in February while City welcomed back Joe Hart and the keeper made his presence count.
The home side made a shaky start with David Luiz picking up a yellow card in the first minute, which will rule the Brazil international out of the second leg.
Luiz, however, won PSG a penalty when he was brought down by Bacary Sagna in the 12th minute, only for Hart to deny Ibrahimovic with a sharp diving save to his right — his third straight penalty save in the competition.
It was a measure of revenge for Hart, who in 2012 conceded four Ibrahimovic goals as Sweden beat England 4-2 in a friendly.
Ibrahimovic looked nervy as he missed the target midway through the first half with only Hart to beat having been nicely played in by Thiago Motta in what was a scrappy start by PSG, whose normally neat passing game lacked accuracy.
After Blaise Matuidi, who will also miss the second leg after being booked, lost the ball in midfield, Fernandinho played De Bruyne through and the Belgian fired past Kevin Trapp to open the scoring.
Ibrahimovic, however, levelled three minutes later, capitalising on a bizarre City blunder.
Hart played a goal kick to a Fernando, who dithered on the ball before his pass hit the Swedish striker`s outstretched foot and rolled into the empty net.
PSG went ahead in the 59th minute when Hart palmed away Edinson Cavani`s header into the path of Rabiot, who tapped in.
Fernandinho levelled with 18 minutes remaining, latching onto Bacary Sagna`s cross after Aurier and Thiago Silva failed to clear.
Real Madrid suffered their first defeat in the Champions League this season when they were surprisingly beaten 2-0 at VfL Wolfsburg in their quarter-final first leg on Wednesday.
The Germans were celebrating a memorable last-eight debut after Ricardo Rodriguez`s penalty in the 18th minute and Maximilian Arnold`s strike in the 25th stunned the visitors only four days after their `Clasico` win in Spain over Barcelona.
Despite making just one change to the lineup that started against Barca, Real coach Zinedine Zidane`s team will now go into the return leg in Madrid next week with a clear disadvantage.
The Spaniards, who also saw Karim Benzema limp off with a foot injury in the 40th minute, enjoyed a strong start but never recovered from the quick two-goal strike by the Wolves and were lucky not to have conceded a third in the second half.