PSG manager Laurent Blanc introduced Cabaye, who arrived from the English Premier League on a reported €23m deal, to the Parc des Princes in the 68th minute.
The 28-year-old French international wasted no time in making his presence felt, in icy wet conditions, with an attempt flying off Bordeaux goalkeeper Cedric Carrasso's crossbar.
Ten minutes before Cabaye made his debut PSG took the lead through their star Swedish striker Zlatan Ibrahimovic who picked up a cross from Brazilian Lucas to fire home from close range his 18th goal of the season.
The win - the capital club's 16th of the season - stretched their lead over Monaco, away to Lorient on Saturday, temporarily to six points. Bordeaux remain in seventh, 20 points off the leaders.