Marco Parolo scored twice as Lazio heaped more woe on Milan, who had Philippe Mexes sent off in a 3-1 defeat.
Luca Rossettini scored at both ends of the field, but ended up on the winning side as Cagliari beat Sassuolo 2-1.
Juventus moved five points clear in Serie A with a 4-0 win over Hellas Verona on Sunday, while Sampdoria beat Parma.
A last-gasp penalty from Ioannis Fetfatzidis denied Sassuolo victory as Genoa came from behind three times to earn a point.
Nigel de Jong scored a late winner as AC Milan edged past Sassuolo 2-1 in their Coppa Italia last-16 clash.
Kamil Glik headed home a deserved late equaliser for Torino as 10-man AC Milan's fortune finally ran out at the Stadio Olimpico.
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