The Ligue 1 leaders, who are also through to the last 32 of the French Cup, went ahead courtesy of Pastore's first-half strike only for Andre Poko to equalise in the second period.
But fellow midfielders Rabiot and Matuidi found the back of the net in the 85th and 88th minutes respectively to see PSG through with Pastore putting in a man-of-the-match performance.
PSG, who started with centre back Alex and forwards Ezequiel Lavezzi and Edinson Cavani on the bench, relied on Pastore's talents to subdue a solid Bordeaux team.
Argentina international Pastore, who has only shown glimpses of his brilliant best since joining from Palermo in 2011, scored from close range on the stroke of halftime after being set up by Lucas.
Poko levelled three minutes into the second half after stealing the ball off Rabiot, who made amends by firing home after collecting Pastore's brilliant lobbed pass.
The irrepressible Pastore also started the move for the third goal, which was scored by Matuidi from point-blank range from substitute Cavani's pass.
On Wednesday, Nantes welcome Nice, second tier Troyes host Evian Thonon Gaillard and Olympique Marseille visit Olympique Lyon in their quarter-final ties.