The French champions won 2-1 at the Parc des Princes having thrashed the German side 4-0 in the last-16 first leg, with Marquinhos and Ezequiel Lavezzi wiping out the visitors' early strike by Sidney Sam.
Sami Hyypia's Leverkusen, who finished with 10 men after Emre Can picked up a second yellow card in the 68th minute, were also hampered by Simon Rolfes's missed penalty in the first half.
PSG, who have now won their last six games in all competitions, could have gone through even more easily had Ibrahimovic not missed a couple of clear chances either side of the interval. "We played one of our worst first halves since the beginning of the season," fullback Christophe Jallet told French TV. "There was a lot of waste but we found the mental strength to equalise and then in the second half we were in control."
Rolfes said their battle was as much psychological as physical. "It's not easy playing a match like this when you know that you are out, but for us it was about honour and prestige," he said.
Before kick-off, police were called to central Paris to break up fighting between Parisian and German fans.