The big-spending Ligue 1 leaders looked to be strolling into the quarter-finals when they took the lead in the 10th minute through Ezequiel Lavezzi and his Argentina team-mate Javier Pastore added a second goal two minutes before half-time.
Valencia improved after coach Ernesto Valverde made a couple of astute changes at the break and it was no more than the Spanish team deserved when centre-back Adil Rami surged into the area and volleyed home from close range in the 90th minute.
Ibrahimovic was then shown a straight red card for a wild lunge on defender Andres Guardado in the second minute of added time and he will be suspended for the second leg in Paris on March 6.
"I don't think we relaxed at the end and we could even have scored a third goal on a couple of occasions," PSG coach Carlo Ancelotti told a news conference.
"The team played a good match. We controlled the ball well and I am pleased with our performance."
With former England captain David Beckham watching his new PSG team from the stands, Valencia had more of the ball in the early stages without really threatening Salvatore Sirigu's goal.
The home team were dealt an early blow when Lavezzi exchanged passes with Pastore before racing past his marker into the area and blasting the ball into the net.
Lucas, who struck a long-range effort against a post moments before Lavezzi's goal, then set up the second goal.
The Brazilian burst into the box from the right and pulled the ball back for fellow midfielder Pastore to send a first-time shot past goalkeeper Vicente Guaita.
Valverde hauled off ineffective midfield pair Ever Banega and Jonas at half-time, throwing playmaker Sergio Canales and forward Nelson Valdez into the fray.
The effect was immediate as Valencia looked more dangerous going forward. PSG were also waiting to catch them on the break and Lavezzi and Ibrahimovic went close to adding a third before Rami's strike and the volatile Swede's dismissal.
The sending-off occurred deep in Valencia's half when he was dispossessed trying to shield the ball and he reacted by lunging at Guardado with studs raised and the linesman standing a few metres away.
Valencia had won all eight of their European home games against French opposition before Tuesday and were unbeaten in nine Champions League matches at the Mestalla since a 1-0 defeat to Manchester United in September 2010.
Qatari-backed PSG, who have spent around 250 million euros in the transfer market in the past four seasons, turned in an efficient first-half display and the obvious quality of their players was the difference between the sides.
Rather than splurge tens of millions on strengthening their squad, cash-strapped Valencia have been forced year after year to sell their best players including David Villa, David Silva and Juan Mata.
Roared on by their vocal fans they forced their way back into the tie to give themselves a lifeline for the trip to Paris in three weeks' time.
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