Khazri, the Tunisia midfielder, set up Florian Thauvin for the opener on the stroke of half-time following a 50-metre run then put Anthony Modeste through in the box in the 56th after Lisandro Lopez had levelled two minutes earlier.
Thauvin scored his second just after the hour following a fine team move and Khazri found the top corner with a splendid curling shot to wrap it up with three minutes left.
"I don't know how to explain what happened in the first half," Lyon's captain, Maxime Gonalons, who was playing his 100th league game, told Canal Plus.
"We were badly positioned on their goal. We tried to bounce back after the break but we made too many mistakes tonight.
"We have never said we were chasing the title. We have a very young squad, we lack experience. We will fight to keep the second spot, we'll do everything."
In the the day's early kick-off, Bastia, who had already conceded 52 goals before the game, surrendered possession and banked on tight defence and their forwards' pace on the counter-attack.
Thauvin took advantage of Lyon's lethargy to add the third and Khazri completed his side's fine work as 14th-placed Bastia moved six points above the relegation zone on 33.
