Sweden international Ibrahimovic opened the scoring after just six minutes when he rose highest to head home Lucas Moura's cross.
The striker then turned provider for his teammate Lavezzi on 19 minutes when he laid in the Argentina forward, who ran past Francois Modesto before finishing it off.
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Yohan Cabaye almost got in on the act when he shaved the crossbar on 67 minutes with a dipping half-volley.
Lavezzi made it 3-0 with two minutes of normal time remaining when he reacted quickest to Ibrahimovic's knockdown to round the goalkeeper before slotting into an empty net.