MILAN (AP) -- Mauro Icardi scored his first ever hat trick as Inter Milan thrashed 10-man Sassuolo 7-0 on Sunday for its first victory of the fledgling Serie A season, while AC Milan won 5-4 at Parma in a highly entertaining match, which saw both teams reduced to 10 men.
New signing Paolo Osvaldo netted twice and Mateo Kovacic also recorded his first league goal for Inter, while Fredy Guarin capped off a fantastic day for the Nerazzurri.
Sassuolo, which lost at home by the same scoreline in its first meeting with Inter last season, also had forward Domenico Berardi sent off for an elbow on Juan Jesus.
"I never scored a hat trick, either with Sampdoria or with Inter," Icardi said. "Today is the first and it's something nice, because I managed to do it at San Siro. This hat trick is for my family, which is always with me."
Jeremy Menez scored the pick of the night and took his tally to three goals in two matches as Milan started with two straight wins for the first time in eight years. That season it also won against Lazio and Parma.
Next weekend's match will be a true test of the merits of Milan and new coach Filippo Inzaghi -- who is in the first season of his senior managerial career -- with the Rossoneri facing three-time defending champion Juventus and former boss Massimiliano Allegri.
"It was an incredible match," Menez said. "The fans saw a beautiful match tonight. We never gave up, in football scoring a goal more is what matters."
Elsewhere, Gonzalo Higuain missed a penalty as Napoli went down to a surprise 1-0 loss at home to Chievo Verona, and Lazio beat Cesena 3-0.
Fiorentina drew 0-0 with Genoa and Atalanta won 2-1 at Cagliari, while Sampdoria beat Torino 2-0 in the lunchtime kickoff and said it will donate half of the ticket sales to ALS research.
After kicking off its season with a goalless draw at Torino, Inter was keen for victory in front of its fans.
The San Siro faithful had to wait less than four minutes for Inter to open its goal account for the season. Icardi beat the offside trap to run onto Kovacic's through ball and although his first attempt was blocked by Andrea Consigli, he rounded the goalkeeper and bundled it into an empty net.
Kovacic netted his first Serie A goal in the 21st minute following a couple of flicks from Icardi and Osvaldo.
The Sassuolo defense looked shaky and it left Icardi in acres of space on the half hour to control Hernanes' pass and curl into the bottom right corner from outside the area.
It was then Osvaldo's turn to open his Inter account four minutes from halftime after Dodo's initial shot was blocked by Consigli.
Icardi completed his hat trick eight minutes into the second half, with Kovacic again the provider and any hope Sassuolo had of keeping the scoreline down evaporated shortly afterwards when Berardi was dismissed.
Guarin generously set up Osvaldo for the former Southampton forward's second before getting on the scoresheet himself as Inter matched last season's result.
City rival Milan was eager to build on its opening 3-1 win against Lazio.
Giacomo Bonaventura scored on his debut but Milan was caught napping as former forward Antonio Cassano immediately leveled. Keisuke Honda's second goal in two matches and a penalty by Menez gave Milan a comfortable halftime lead.
Felipe pulled one back for Parma before Milan was reduced to 10 men after Daniele Bonera was shown a second yellow.
Nigel de Jong grabbed a great individual goal with a run from the halfway line after Parma lost possession and Menez bettered him with a backheel from close range after flicking the ball around the goalkeeper at the byline.
Alessandro Lucarelli had pulled a goal back for Parma before Felipe was also dismissed for a second booking.
There was a nervy final few minutes for Milan when Parma reduced the gap even more following a De Jong backpass from near the center of the pitch which Lopez completely missed.