Meanwhile Nemanja Vidic was sent-off on his debut for Inter Milan in their 0-0 draw at Torino yesterday.
New Rossoneri signing Fernando Torres was in the stands alongside president Silvio Berlusconi, to watch goals from Keisuke Honda, Sulley Muntari and a Jeremy Menez penalty give Inzaghi's men three well-earned points.
"Today we won, but we mustn't delude ourselves," Inzaghi told Sky Sport Italia.
"For the first hour we played a near perfect game, then we struggled a bit against Lazio, who I think will be the surprise team this season.
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Initially, Milan looked nervous in defence with Lazio keen to exploit centre back Daniele Bonera, who had lined up in the left back position, but it wasn't long before any trepidation was extinguished, as Milan opened the scoring after just seven minutes.
Stephan El Shaarawy latched on to a hopeful long ball on the left, rode the challenge of Stefan de Vrij, before sliding the ball to the in-rushing Honda on the right, who put it through the legs of Etrit Berisha.
Ten minutes after the restart, Milan doubled their advantage against the run of play. A simple cross from Ignazio Abate on the right, bounced in the six-yard area, inviting the unmarked Muntari to poke it home.
Then, just after the hour mark, De Vrij brought down Menez in the area with the slightest of touches and the Frenchman stepped up to take the resulting spot kick and fired low into the goalkeeper's right-hand corner.