Ghana striker Jordan Ayew scored his ninth goal of the season but it was not enough to save Lorient from defeat as they lost 3-2 to PSG.
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It looked set to be a comfortable evening for PSG when Ibrahimovic opened the scoring from the spot in the fourth minute.
But Lorient remained in the game and drew level midway through the second half courtesy of a fine Jordan Ayew strike.
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Nevertheless, Paris reclaimed the lead with eight minutes remaining when Ibrahimovic scored another penalty, and the Swedish striker wrapped up the points in stoppage time as he completed his hat-trick to take his tally for the season to 17 goals in Ligue 1, and 23 in all competitions.
Lorient, meanwhile, remain five points above the relegation zone for now.