The prolific Sweden international was forced off just 15 minutes into the game at the Parc des Princes but his fellow forward sealed victory with a second-half goal
The champions were held to a 2-2 draw at Reims in their first game of the new league campaign, but proved to be too strong for Bastia as goals from Lucas Moura and Edinson Cavani secured all three points in Paris.
PSG's victory came at a cost, though, as talismanic striker Zlatan Ibrahimovic was substituted only 15 minutes in after taking a knock to either his back or side and coach Laurent Blanc will be hoping the injury is not serious, having already lost defender Thiago Silva to a hamstring problem this week.
It was a comfortable victory for the Parisian giants, who were rewarded for a dominant display with a goal in each half from Lucas and Cavani, as former PSG assistant coach Claude Makelele suffered his first Ligue 1 defeat since taking over at Bastia.
Big-money signing David Luiz made his Ligue 1 debut alongside Marquinhos at the heart of the PSG defence in the absence of Silva.
El-Hadji Ba was handed his league debut for Bastia, who played out a thrilling 3-3 draw with Marseille in their first league game of the season, following his move on a season-long loan from Sunderland.
PSG made a bright start and Cavani, who has been linked with Liverpool, had a chance to open the scoring just three minutes in, only to see his shot deflected over the crossbar.
There was concern for PSG when Ibrahimovic required treatment after seemingly taking a knock to his side after only six minutes and the prolific striker was eventually replaced by Ezequiel Lavezzi.
Brandao spurned a chance to give Bastia a shock lead when he rose to head wide of the far post and he was made to pay when Lucas put PSG in front in the 26th minute.
Gregory van der Wiel was the architect, swinging over an inviting cross from the right and an unmarked Lucas clinically volleyed home from six yards out.
Lavezzi then fired wildly over the bar seven minutes before the break as PSG pushed for a second goal.
New signing Serge Aurier replaced Van der Wiel at the break and the home side picked up where they left off when Bastia were almost caught out by a quick-free kick, which allowed Lucas to race clear but fail to apply the finish as he fired wide of the near post.
Makelele's side failed to heed the warning, though, as they were again caught cold when Marco Verratti superbly picked out Cavani with a quick free-kick.
Cavani still had plenty to do as he took an excellent touch to control the ball, but he rifled home with his right foot as he was falling to the turf to seal PSG's win just before the hour mark.
The Uruguay forward looked like he had a point to prove as he tried his luck with a 25-yard free-kick, but two goals were more than enough for PSG.