The visitors took the lead after just three minutes when a great team move culminated in Marco Verratti threading the ball through to Kylian Mbappe, whose powerful drive beat Matz Sels en route to the back of the net.
Despite being evenly matched by the hosts, PSG went on to double their lead on the stroke of half time, with Neymar's ferocious drive kept out by Sels but flicked back into play by Mbappe and slotted home by Edinson Cavani into an empty net.
Unai Emery's charges were quick out of the starting blocks in the second half as Cavani rattled the woodwork on 50 minutes and had a goal disallowed nine minutes later amid a flurry of chances from the visitors.
Eventually the third man in PSG's stellar attacking trio got himself on the scoresheet as Neymar won a free kick and, instead of curling the ball above and beyond the wall, slotted it underneath the Anderlecht players - who had already jumped - and into the net.
The Ligue 1 giants went on to add a fourth two minutes from time as a miscued clearance saw Angel Di Maria claim the ball, dribble into the 18-yard box, and dink an effort over the onrushing keeper.
The result sees PSG cement their hold on first place in Group B with nine points from three games, as well as 12 goals scored and none conceded, while sorry Anderlecht sit bottom without a point or a goal to their name.