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 capitalized 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 an 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 fullback 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 the club's 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 its rhythm and Lucas Moura was only denied an attempt at goal by some desperate Bordeaux defending.
However, Laurent Blanc's side did find the breakthrough at the half-hour mark.
Ibrahimovic was the architect, as 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 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 leveled 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 center of the box.
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 defense stood motionless and rounded the goalkeeper with a neat feint before rolling into the unguarded net.
PSG was 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.