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Lens were the first side to threaten when Lalaina Nomenjanahary picked out Chavarria, but he somehow could only skew the ball wide of goal from the six-yard box.
The away side sought to hit back despite being limited in their attacking play, with Ryad Boudebouz letting fly from distance with an effort which flew just over the crossbar.
Lens went a goal to the good five minutes before the break as Chavarria made amends by tucking into the bottom corner, following a cross from Wylan Cyprien.
However, Bastia mounted a fightback after the break, leaving Gillet to latch on to Mathieu Peybernes's cross and convert into the bottom corner to earn his side a point.