Lille's Jonathan Delaplace was the first to make a meaningful chance when he forced a save down low at the bottom corner following a shot from distance.
Floyd Ayite produced a dangerous moment from a corner as he found Sebastien Squillaci rising in the box, but the defender headed his effort over the bar.
The hosts took the lead though after the 39th minute when Franck Beria found Origi with room outside of the area, allowing the striker to drill home a standout effort into the bottom corner from distance.
Bastia keeper Alphonse Areola was luckily on hand just before the break to prevent the score from being 2-0 at half time, with the keeper pulling off a good save to stop Pape Souare's long-ranger.
Full-back Simon Kjaer had the chance to extend Lille's lead in the second half, with the defender striking wide with his right from the right side of the box.
Hervin Ongenda thought he'd forced an equaliser just before the final whistle, only for Lille keeper Vincent Enyeama to become the hero with a world-class save down at his right corner.