The Swede and the Brazilian were both on target, as Yohan Cabaye made his first appearance in a PSG jersey following his midweek move from Newcastle United
Zlatan Ibrahimovic made the breakthrough just before the hour mark and Alex sealed victory for the home side with two minutes to go.
Laurent Blanc's men, who were held to a disappointing draw by Guingamp last weekend, knew defeat on Friday would give second-placed Monaco, in action against Lorient on Sunday, the chance to draw level at the top of the table.
The defending champions struggled to break down a Bordeaux side that would have moved into fourth with a win, but ultimately prevailed thanks to their perseverance and patience.
New signing Yohan Cabaye was left on the PSG bench following his move from Newcastle United, while Thiago Silva returned to the starting XI after missing the draw with Guingamp through injury.
Julien Faubert came in for Bordeaux, who named former PSG striker Guillaume Hoarau among their substitutes.
PSG dictated play from the start and were unfortunate not to be awarded a penalty inside the first five minutes when Carlos Henrique appeared to haul down Ibrahimovic in the area.
Goalscoring opportunities proved rare for the remainder of the half, Edinson Cavani heading over after 12 minutes as the hosts laboured to try to find a breakthrough.
Bordeaux's produced a stern defensive effort up until half-time, but the visitors' resistance was broken by Ibrahimovic.
The Sweden international was handed the simple task of tapping in from point-blank range following good work down the right from Lucas, who delivered a pinpoint cross for Ibrahimovic to score his 29th goal of the campaign.
Blanc's side came close to doubling their advantage minutes later as Javier Pastore's drilled effort was well saved by Cedric Carasso.
Pastore was replaced shortly after that chance, the Argentina international making way for Cabaye to make his debut after 68 minutes.
PSG suffered a blow only seven minutes later as Cavani limped off to be replaced by Ezequiel Lavezzi.
Cabaye almost marked his PSG bow with a goal as he headed against the post from a Ibrahimovic cross, but PSG did make sure of the points with two minutes remaining, Alex volleying home Lucas’ corner at the near post.