The Sweden international struck after 17, 22 and 36 minutes - the eighth quickest treble in Champions League history - and added PSG's fifth just past the hour to lead the French champions to victory at the Constant Vanden Stock Stadium.
His third goal was so good it earned a round of applause from the generous home fans, and Ibrahimovic - seldom afraid to play to the galleries - applauded them back.
Uruguayan striker Edinson Cavani was also on the scoresheet in the second half as Laurent Blanc's team moved to nine points from three games, top of the group and within sight of the knockout stages.
"I feel good," Ibrahimovic told UEFA's official website. "This year we are stronger, we have stronger players. We could win the competition but remember that the further you go, the harder it is."
Anderlecht, once UEFA Cup champions, had no answer to Ibrahimovic's power and finishing, and are bottom of the section after three consecutive defeats.
Ibrahimovic's feats made him only the fourth player to score four in one Champions League game, and he now has 10 goals in the past five games for club and country.
He missed a presentable early chance, too, stabbing wide from an angle with only keeper Thomas Kaminski to beat.
Thereafter he could hardly miss.
He set PSG on their way to their biggest away win in European competition by outwitting the Anderlecht defence, pulling off his marker with subtle movement to slide home Gregory van der Wiel's low centre at the far post.
Van der Wiel was provider again five minutes later, surging into space on the right flank and crossing for Ibrahimovic, who finished into the bottom corner with a wonderful improvised flick of his right boot.
The highlight of the match arrived nine minutes before half-time, when Ibrahimovic pounced on a loose, bouncing ball 25 yards out and produced a right-foot half-volley that kept bending away from Kaminski's outstretched hand until it slammed into the roof of the Anderlecht net.
The procession continued within seven minutes of the restart, when defender Chancel Mbemba slipped, allowing Blaise Matuidi to square for Cavani, who slotted home.
Ibrahimovic's fourth and PSG's fifth was another clinical finish.
The 32-year-old latched on to a lofted Thiago Motta pass down the right, cut inside to the area, and beat Kaminski with another half-volley that went in off the far upright.
Anderlecht came close to a consolation when Luka Milivojevic's shot took a deflection and PSG keeper Salvatore Sirigu was forced into a reflex save.
The only comfort for the home fans was that Ibrahimovic went easy on them in the final minutes.
Another delicious piece of skill allowed him to drag the ball back before chipping a shot on to the roof of the net, and then Kaminski reclaimed some pride, making a double save from Ibrahimovic, who realised enough damage had been done and leant down to check the keeper was not hurt.
- Sports & Recreation
- Edinson Cavani
- Thomas Kaminski