With the game seemingly heading for a draw, Fernando Aristeguieta grabbed the winner with a close-range finish as the match headed towards injury time.
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Saez's goal came seven minutes after the restart when he hit a right-footed effort high into Remy Riou's corner.
However, Nantes had their response eight minutes later when Surge Gakpe supplied Bedoya, who sent a left-footed effort right down the middle on the edge of the box.
Aristeguieta claimed the winner late on as Michel Der Zakarian's side closed the gap on Marseille in the Europa League slot to just one point.