Ibrahimovic was the standout performer as PSG maintained its perfect record in Brussels.
The in-form Sweden striker completed his first ever UEFA 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 an unlikely lead.
Defending champion Bayern Munich swept aside Viktoria Plzen 5-0 at the Allianz Arena to remain favourite 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.
Manchester City is second behind Bayern after Sergio Aguero's double saw it battle back to beat CSKA Moscow 2-1 in the Russian capital.
Zoran Tosic put CSKA ahead after 32 minutes but Aguero's double arrived within 10 minutes.
Keisuke Honda was denied a leveller in the final minute of injury-time by City goalkeeper Joe Hart at close quarters.
Galatasaray got its 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 leader 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.
Manchester United put its league woes to one side with a 1-0 win over Real Sociedad to keep it top of Group A.
Inigo Martinez's own goal after two minutes was enough, although United had the chances to win more comfortably.
Bayer Leverkusen is a point behind the English champion after it 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.