Ryan Boudebouz set the tone after six minutes with his first goal for the club before Whabi Khazri put the hosts in the driving seat from the penalty spot.
Mathieu Coutadeur's strike gave Lorient some hope before the interval, but Milos Krasic and Christian Romaric put the result beyond doubt in the second half before Larry Azouni's dismissal compounded a woeful night for the visitors.
Boudebouz rifled home from the edge of the box to cap a lively start from Bastia, with Khazi doubling their lead from the spot after he had been fouled by Coutadeur with 23 minutes gone.
Coutadeur made amends eight minutes later with a composed finish past Mickael Landreau to reduce the deficit.
But Krasic restored Bastia's two-goal cushion 14 minutes into the second half, dancing past two players before finding the bottom corner.
Romaric put the icing on the cake with a towering header, with Azouni given his marching orders just eight minutes after coming off the bench.
'People will remember us because we got to No.1 in the world rankings and achieved great things - but our biggest regret is that we didn’t win anything': Ex-Everton star Kevin Mirallas opens up on 'honour' of being part of nation's golden generation
‘I’m sure we’d have finished in the top four or five if he hadn’t joined Chelsea in January. Him leaving damaged the team, but we couldn’t stand in his way’: Alan Curbishley reflects on failed Champions League dream after selling key player
