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The hosts, who started the evening outside the bottom three only on goal difference, made a lively start to the match and almost took the lead inside eight minutes when Jerry Mbakogu's looping header was saved by Alberto Pelagotti.
Empoli were dealt a blow in the 25th minute when Levan Mchedlidze was shown a straight red card for violent conduct, poleaxing Marco Crimi with a heavy challenge that left the opposing player needing treatment.
More controversy followed as Carpi coach Fabrizio Castori was given his marching orders in the wake of the incident for entering the field of play in an attempt to confront the Empoli players.
The home side almost made their numerical advantage count in the 67th minute when Simone Romagnoli's right-footed drive came back off the crossbar, while Manuel Pucciarell came close for the visitors at the other end moments later.
Further chances fell both ways, but it was Carpi who dug deepest to snatch a winner in the 85th minute. Lorenzo Pasciuti played a dangerous ball into the box and Lasagna was on hand to turn it in from close range.
Both sides finished the match with 10 men as Lorenzo Lollo was sent off in the 90th minute after collecting a second yellow card, but his dismissal had no impact on the outcome of the match.
The win sees Carpi open up a three-point gap in the table between themselves and 18th-placed Palermo, who have a vastly inferior goal difference. The result also relegated bottom club Hellas Verona, despite their shock 2-1 win over AC Milan this evening.