Ibrahimovic completed his first Champions League hat-trick in a devastating 18-minute spell before half-time to ensure the French champions easily maintained their perfect record in Group C.
Edinson Cavani got in on the act after half-time, thanks to a defensive blunder, before Ibrahimovic became just the fourth player to score four times in a Champions League match.
The Sweden striker has now scored 10 goals in his past five games for club and country.
The goal that completed his hat-trick was the pick of the bunch, and loomed as an early contender for goal of the season.
After Gregory van der Wiel had set-up his opening two goals, Ibrahimovic took it upon himself to claim his third as he smashed an unstoppable 30-yard volley into the top corner.
Anderlecht, who remain without a point, had forced PSG goalkeeper Salvatore Sirigu into some early action when Aleksandar Mitrovic and Matias Suarez got early sights on goal.
But from there Ibrahimovic took over.
The 32-year-old should have had his first on 12 minutes when he ran onto Marco Verratti's pass and, after rounding goalkeeper Thomas Kaminski, could only find the side netting.
It mattered little as the opener came five minutes later when Van der Wiel found space down the right and delivered a low cross that Ibrahimovic turned in after breaking off his marker to the back post.
The same pairing then combined for PSG's second, although this time Ibrahimovic added his usual flamboyance.
Van der Wiel was again given too much room and while Ibrahimovic was this time tightly marked he cushioned a back-heel past the goalkeeper with the aid of a slight deflection.
There was no subtly about Ibrahimovic's third on 36 minutes, however, as home goalkeeper Thomas Kaminski - on his 21st birthday - was left flapping at air.
A weak defensive clearance fell only into the danger area where the lurking Ibrahimovic suddenly sprang to life to smash his thunderbolt drive past Kaminski.
Anderlecht's pain was not complete though and it was their own fault that a fourth was gifted to PSG.
Chancel Mbemba slipped over with no apparent danger around him just outside the area, and after failing to recover, Blaise Matuidi nicked in and slid the ball for Cavani to score past an exposed Kaminski.
Ibrahimovic's fourth then arrived on 62 minutes as he raced onto the ball in the area and finished into the far corner.
He had a chance to join Lionel Messi as the only player to score five times in a Champions League game moments from the end, but was denied by a stunning Kaminski double save.
It was about the only record to elude the PSG skipper on the night, with his side also able to celebrate their biggest ever away win in Europe.