The hosts, who were beaten 7-2 by Nice in midweek, came close to breaking the deadlock early on when Sambou Yatabare curled just wide of the post.
Guingamp broke the deadlock just after the half hour mark when a corner caught Alphonse Areola out of position, which resulted in Guillaume Gillet inadvertently diverting into his own net as he looked to clear Yatabare's effort from close range.
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Mustapha Diallo could have put the result beyond doubt with less than 20 minutes of normal time remaining, but he sent a shot over after latching onto a loose ball in the box, before heading wide moments later.
Bastia's desperate attempts to find a way back into the game late on ended in disappointment as Guingamp held on to pile more pressure on Claude Makelele and his players.