The Brazilian curled in a brilliant 30-yard free-kick after just five minutes at the Parc des Princes before sliding in Edinson Cavani to double the lead seven minutes later.
Thomas Meunier’s excellent side-footed finish made it 3-0 to PSG on 21 minutes, but Bordeaux hit back on the half hour as Younousse Sankhare applied the final touch to a slick team move.
PSG were then awarded a penalty, the first since a row between Neymar and Cavani over spot-kick duties overshadowed a 2-0 win against Lyon a fortnight ago, with Neymar this time stepping up to convert.
Julian Draxler volleyed in a superb fifth before half-time and Kylian Mbappe added another on 58 minutes, while Malcom scored a late penalty for Bordeaux, as PSG pulled three points clear of defending champions Monaco at the top.
Unai Emery rested captain Thiago Silva for the visit of third-place Bordeaux, who arrived in the capital trailing PSG by just four points after seven matches.
The hosts brushed aside five-time European champions Bayern Munich 3-0 in midweek and the gap in class on Saturday was evident from the start against Jocelyn Gourvennec’s team.
With Monaco dropping points in Friday’s 1-1 draw at home to Montpellier, PSG immediately signalled their intent as three quick-fire goals left Bordeaux seeking to limit the damage.
Neymar struck early as his magnificent free-kick flashed beyond a helpless Benoit Costil, with the Brazilian then playing in Cavani to poke in his eighth league goal of the season on 12 minutes.
PSG were further in front when Yuri Berchiche’s cross from the left skipped past Mbappe but Meunier ran onto it and the Belgian international steered past Costil.
Bordeaux replied on 31 minutes after Theo Pellenard demonstrated remarkable composure to thread in Nicolas de Preville who squared for Sankhare to tap into an empty net.
But a senseless handball from Otavio gifted PSG a penalty and Neymar, rather than Cavani whose effort in the Lyon win on September 17 was saved, tucked away the spot-kick for his sixth league goal.
Draxler made it five in style on the stroke of half-time when he fired in from Mbappe’s floated cross, and the French teenager notched a goal of his own on 58 minutes after he was released in behind the defence by the German.
Bordeaux substitute Alexandre Mendy smacked the outside of the post on 69 minutes while a shot from Neymar whistled just wide after a clever exchange with Draxler.
Brazilian Malcom, who extended his contract with Bordeaux until 2021 this week, netted a consolation in the final minute after Jonathan Cafu was fouled in the area by Meunier.
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