The 21-year-old attacker netted for the fourth successive game, slotting home a pass from Zlatan Ibrahimovic, before Marquinhos bagged what proved to be the game's decisive goal
Bahebeck, a goalscorer in all three of PSG's previous friendlies, continued his impressive form in the build up to the new campaign, as he netted the opener at the Stade de la Mediterranee in Beziers before Marquinhos wrapped up the win.
A late goal from teenager Franck Honorat gave Nice something to take from the game, but Laurent Blanc's side had already done enough by that stage.
Following wins for PSG over Hartberg and Videoton before losing to Red Bull Leipzig during pre-season, Nice promised to provide sterner opposition for the Ligue 1 champions.
However, Blanc's side started brightly and forged ahead in the third minute when Bahebeck slotted in at the far post after being cleverly played in by last season's Ligue 1 top scorer, Zlatan Ibrahimovic.
Their lead was doubled nine minutes before half-time through centre-back Marquinhos.
Bahebeck was involved again, his corner being met by the Brazilian with a powerful downward header past Nice goalkeeper Mouez Hassen.
Nice, to their credit, produced a much-improved performance in the second half and they were rewarded in the 73rd minute with a well-taken goal from 17-year-old striker Honorat.
But for all their endeavour, Claude Puel's side could not find an equaliser.