The 25-year-old Brazilian’s opener for the Ligue 1 pacesetters was a sumptuous free kick from 25 metres.
His slick pass then set up Edinson Cavani to double the advantage after 12 minutes. It was the Uruguay international’s eighth league goal of the season.
The contest was effectively over 10 minutes later when Thomas Meunier flicked home to make it 3-0.
Bordeaux, who were unbeaten, travelled to the capital in third place four points behind PSG. They reduced the deficit on the half hour when Younousse Sankhare slotted past goalkeeper Alphonse Areola.
Any hopes though of a comeback were extinguished in the five minutes before half time with goals from Neymar and Julian Draxler.
Neymar’s came from a penalty given for a handball. It was the first spot kick awarded to PSG since an on field row between Neymar and Cavani over who should take penalties overshadowed a 2-0 win against Lyon a fortnight ago.
Back then Cavani demanded the ball and missed the target. This time Neymar had the honour and converted to claim his sixth league goal for PSG since joining for 222 million euros from Barcelona.
"For me the important thing with penalties is to score them," said PSG coach Unai Emery. "The main thing is the two of them see the opportunity and they both can take penalties. The decision is down to those two. We've already spoken about it internally."
After the first half goalfest, the second period was cruise control for PSG who swept past Bayern Munich 3-0 on Wednesday night in the second game of their Uefa Champions League campaign.
Kylian Mbappe, who was a thorn in Bayern’s side, made it 6-1 before Malcom salvaged a modicum of respectability for the visitors with a late penalty.
"It was a good win against a team that was still undefeated," said Mbappe. "We don't need to send a message, we're just concentrating on ourselves. We could still do better, we're not going to be picky, but there's still room for a bit more."