Nice, Bastia each get wins in Ligue 1
Bastia hadn't scored away from home in its previous five games but Ilan ended that barren run when he acrobatically sent home a cross from Jerome Rothen in the 20th minute.
Florian Thauvin doubled Bastia's lead three minutes into the second half with another spectacular goal, following an assist from Anthony Modeste.
Reims pulled one back in the 63rd when Gaetan Courtet was left unmarked to slot home Diego's cross.
However, it was Bastia that looked the more likely to score again and Modeste had the ball in the back of the net in the final minute, but it was ruled out for offside.
The loss extended Reims' run without a victory to 13 matches.
Dario Cvitanich opened the scoring on the stroke of halftime and the floodgates opened after the break, with Cvitanich scoring again to add to goals from Renato Civelli, Valentin Eysseric and Didier Digard.