The in-form Sweden striker completed his first ever Champions League hat-trick in a devastating 18-minute burst during the first half, with his third an early contender for goal of the season.
Ibrahimovic raced onto a headed clearance and smashed an unstoppable 30-yard volley past home goalkeeper Thomas Kaminski - who had a 21st birthday he may not forget.
Edinson Cavani got in on the act after half-time, following a defensive blunder, before Ibrahimovic became just the fourth player to score four times in a Champions League match.
Olympiacos and Benfica trail PSG by five points in Group C after Oscar Cardozo salvaged a late point for the Portuguese side in Lisbon.
Alejandro Dominguez's 29th-minute had given Olympiacos and unlikely lead.
Defending champions Bayern Munich swept aside Viktoria Plzen 5-0 at the Allianz Arena to remain favourites to top Group D.
Franck Ribery scored in either half and with David Alaba, Mario Gotze and Bastian Schweinsteiger also on target it was three wins from three for Pep Guardiola's side, who stay ahead of Manchester City after their win at CSKA Moscow.
Galatasaray got their campaign up and running with a 3-1 rout of FC Copenhagen.
New coach Roberto Mancini secured his first win in charge at the weekend and his side jumped into second in Group B thanks to first-half goals from Felipe Melo, Wesley Sneijder and Didier Drogba. Claudemir pulled a goal back two minutes from the end.
Juventus slipped below the Turkish side following a 2-1 loss to leaders Real Madrid.
Spanish striker Fernando Llorente cancelled out Cristiano Ronaldo's early opener but Madrid's star man fired them back ahead with a 28th-minute penalty.
Bayer Leverkusen moved to within a point of group leaders Manchester United after they beat Shakhtar Donetsk 4-0.
Stefan Kiessling put the 'ghost goal' controversy of the weekend behind him to score in either half with a Simon Rolfes penalty and Sidney Sam strike after half-time serving to overrun Shakhtar.
All of us may think he is an a.s.s, a jerk, a Jacka..., and any other qualification you may come up with but hey I would love to have him at Anfield. Him Suarez and Sturidge with Coutinho and Gerrard providing, WOW!!! If only.- marrowak