It was the hosts who were first to come close after 15 minutes when Yannick Cahuzac sent Sadio Diallo through on goal, but rather than trying to beat the last defender he opted to shoot from range, firing his effort narrowly wide.
Bastia had an even better chance to take a surprise lead shortly afterwards when Allan Saint-Maximin fired a low ball into the box that found Enzo Crivelli, who could only slice his finish wide from close range.
The champions had to wait until shortly before the half-hour mark for their first real sight of goal when Angel Di Maria brought the ball forward before cutting inside and letting fly, but Jean-Louis Leca got down to make a comfortable stop.
Leca was called into action again early in the second half when he denied Di Maria once more, reacting well to save the Argentine's low volley having initially failed to get a big enough punch on Serge Aurier's cross.
After an under-par first half, PSG continued to grow into the game in the second period and David Luiz was the next to threaten with a dipping free kick that was held by the Bastia keeper.
The hosts still carried a threat going forward, though, and PSG were relieved to see the ball squirm narrowly past their post after Gael Danic's curling cross into the middle had caused havoc in the area.
Emery's side finally did find the breakthrough with just over 15 minutes remaining when debutant Jese Rodriguez latched on to a through-ball from Di Maria before being denied by Leca, with the ball falling kindly for Kurzawa to bundle home the rebound from close range.
That proved to be the winner as PSG made a laboured but successful start to their campaign, taking their routine place at the top of the Ligue 1 table nice and early.