Saint-Etienne seemed to be awoken by the goal and made a spirited effort to try and level proceedings that came in the 19th minute.
The Saints were awarded a penalty when Mehdi Zerkane brought down Khazri in the area and the Tunisia international stepped out to dispatch home his spot-kick.
Khazri then gave his side the lead four minutes later when he connected with Adil Aouchiche's cross before firing into the back of the net.
The attacker completed his hat-trick in the 72nd minute, converting from the penalty spot after Jimmy Briand was adjudged to have handled the ball in the area.