The Brazilian struck in the second half following Blaise Matuidi's well-crafted opener to move Laurent Blanc's side one point above Monaco
The Brazilian capitalised on a failed offside trap and an error from goalkeeper Cedric Carraso to seal the points for the champions after Blaise Matuidi had handed them a first-half lead following excellent play from Zlatan Ibrahimovic.
Ludovic Obraniak came closest for the hosts, who toiled hard but created few chances of note, allowing PSG to move one point above Monaco after playing one game more and extend their unbeaten run to 16 matches.
PSG handed a league debut to full-back Lucas Digne, but Edinson Cavani had to settle for a place among the substitutes bench.
Bordeaux named Lucas Orban and Diego Rolan in their starting XI, as Francis Gillot made three changes to the side that lost 2-1 to Saint-Etienne in their last Ligue 1 fixture.
The home side stifled the champions in the early exchanges, but only had an Andre Poko effort that cleared the crossbar to show for their efforts.
But as the game opened up, PSG began to find their rhythm and Lucas Moura was only denied an attempt at goal by some desperate Bordeaux defending, before Ibrahimovic blasted a free-kick over the bar in the 21st minute.
However, Laurent Blanc's side did find the breakthrough on the half-hour mark.
Ibrahimovic was the architect and a neat one-two with Hervin Ongenda led to the Sweden international playing an intricate through-ball to Matuidi on the left. The midfielder’s initial effort squirmed under goalkeeper Carrasso but Matuidi made sure of the goal by prodding home on the line.
As PSG backed off, the game was almost level two minutes before the break when Ludovic Obraniak tested Salvatore Sirigu with a low strike from inside the box, but the Italian saved to preserve PSG’s half-time lead.
Cheick Diabate twice almost levelled at the beginning of the second period, first tamely hitting an effort at Sirigu before forcing Alex into a last-ditch tackle when through on goal.
With the visitors under pressure, Thiago Silva was then fortunate not to concede a penalty when he appeared to handle an Obraniak cross in the centre of the box.
Bordeaux were almost punished further when Ibrahimovic pounced on a Mariano mistake to strike hard at Carrasso from 25 yards, but the advantage was finally doubled in the 64th minute.
Lucas sprung the offside trap to latch onto Marco Verratti's pass. He raced on goal as Bordeaux's defence stood motionless and rounded the goalkeeper with a neat feint before rolling into the unguarded net.
PSG were denied a third with 20 minutes remaining thanks to a wonderful double save from Carrasso. First he palmed away Ibrahimovic's effort from the right-hand side of the box, before getting up well to save Digne's effort with his feet.
Bordeaux completely lost focus in the last 10 minutes as PSG rained a host of chances at the opposition goal, with Ibrahimovic coming closest when he rounded the keeper but could only hit the side netting from a tight angle.
The win extends Blanc's charges' unbeaten run to 16 matches and temporarily moves them top of Ligue 1, a point clear of Monaco, who play Lorient on Sunday.