Lionel Messi was again absent through injury, but the other two stars of Mauricio Pochettino's deadly attacking trident combined to brilliant effect.
Neymar had not scored from open play in Ligue 1 since doing so against Lens in May, but ended that run with two sublime first-half strikes.
Mbappe, who had teed up Neymar's double, got in on the act midway through the second half to ensure late goals from Alberth Elis and M'Baye Niang were not enough for Bordeaux.
It was far from plain sailing for PSG at first, though, as Bordeaux had the better of the opening exchanges, regularly catching the visitors dawdling in their own half.
Yet Bordeaux was soon lamenting its failure to make PSG pay, with Neymar taking Mbappe's floated pass under his spell before drilling a wonderful finish beyond Benoit Costil.
Costil had to be at his best to prevent Mbappe making it 2-0, but could do little to prevent Neymar doubling PSG's tally before the break.
The combination with Mbappe again came to the fore, Neymar playing a slick one-two with the France star before sliding a cool effort into the bottom-left corner.
Mbappe looked set to go from provider to scorer early in the second half, only for Laurent Koscielny to make a fantastic last-ditch block.
He was not to be denied again, though, and he tucked home into a gaping goal after Ander Herrera's pass had set Georgino Wijnaldum away.
Elis's close-range finish gave Bordeaux hope, with substitute Niang then slotting in after a fantastic one-two with Jimmy Briand in stoppage-time, but it was too little too late.