Marseille are looking to rediscover some magic under Argentine coach Bielsa in a bid to unseat arch-rivals Paris St Germain, champions for the last two seasons.
A loss of concentration allowed midfielder Christopher Maboulou to open the scoring for Bastia with the first of his two goals in the ninth minute.
Gignac equalised three minutes later with a header from a cross by Benjamin Mendy and an own goal by Romaric put Marseille 2-1 up at halftime.
Marseille went further ahead with Gignac's second goal, a penalty just past the hour.
However, Claude Makelele's side fought back with a 66th-minute penalty converted by Junior Tallo for a foul on Maboulou, who then equalised with his second goal in the 73rd.
PSG also only managed a 2-2 draw in their opening match at Stade Reims on Friday with a brace from Zlatan Ibrahimovic.
Caen had the biggest win on Saturday, thrashing Evian 3-0, while St Etienne won 2-0 at Guingamp and Nice beat Toulouse 3-2 at home.
(Reporting by Maya Nikolaeva; Editing by Rex Gowar)
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