Meanwhile, Nemanja Vidic was sent-off on his debut for Inter Milan in their 0-0 draw at Torino on Sunday.
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 said.
"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. We have created a good group here, which makes me happy. Even if we lose a few games, it will be against teams who are stronger, not those who have more desire,” he added.
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.
In an opening period with little in the way of goalmouth action, Lazio's only meaningful chance came midway through the half as Miroslav Klose got in behind the Milan defence down the right but his cross deflected off Cristian Zapata only to be easily gathered by goalkeeper Diego Lopez.
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.

But Lazio immediately pulled one back as Filip Djordjevic's near-post flick was deflected in at his near left-hand post by Alex.
Lazio's perseverance got them a penalty in time added on after Antonio Candreva was fouled but Lopez got down low to his right and palmed the midfielder's spot kick away.
Meanwhile, Vidic was having a nightmare in Turin.
He gave away a penalty midway through the first half after pulling down Omar El Kaddouri but Samir Handanovic saved Marcelo Larrondo's resulting spot kick.
Nevertheless, Vidic's debut disaster was compounded as he received a 90th minute red card.
"The referee made a mistake," Inter coach Walter Mazzarri moaned.
"Like they do in England, Vidic applauded when a foul was whistled. His actions were misinterpreted. It was absurd,” he added.      

Rafael Benitez's Napoli left it late to earn a 2-1 win against Genoa as they looked to bounce back from their midweek Champions League exit at the hands of Athletic Bilbao.
Jose Callejon put the away side ahead after three minutes but Genoa's summer signing Mauricio Pinilla headed home a deep Giovanni Marchese cross to equalise just before the break.
The Partenopei won it in the fifth minute of time-added-on as debutant Jonathan de Guzman latched onto a Juan Zuniga long ball in the six-yard box and poked past a statuesque Mattia Perin.
Sassuolo's Simone Zaza scored a Marco van Basten-esque volley against Cagliari as the two sides played out an exciting 1-1 draw. Marco Sau netted for the Sardinians.
Elsewhere, an Antonio Di Natale double helped Udinese to a 2-0 win over Empoli, Palermo drew 1-1 with 10-man Sampdoria, while newly promoted Cesena overcame Parma 1-0.
In Bergamo, Atalanta were held to a 0-0 draw by Verona in what was an utterly dull affair.

Latest News from Sports News Desk