It marked another disappointing evening for former Champions Inter and their manager Simone Inzaghi who has yet to pick up a point at the ground he graced as a player for over a decade and where he managed until 2021.
The former Italy striker, instead, had to play second fiddle, as he did last year when Inter were handed another 3-1 defeat, to Maurizio Sarri, the man who replaced him on the Lazio bench.
"It was a very bad loss," Inzaghi told DAZN. "It was an even game. We had a good first half but Luis Alberto's goal shifted the balance."
Sarri brought on Luis Alberto and Pedro just before the hour mark, shortly after Inter's Lautaro Martinez had canceled out Felipe Anderson's 40th-minute opener.
Luis Alberto restored the Lazio advantage in the 75th minute with a superb shot which left Samir Handanovic stranded in the Inter goal before Pedro wrapped things up four minutes from time.
"This victory is important for us, it's the path we need to follow to progress," said Pedro.
With two wins and a draw in three matches, Lazio take over the top spot in the table, one point ahead of Inter, who won their first two matches.
In Friday's other game, promoted Monza slipped to their third defeat of the season when they lost 2-1 at home to Udinese who collected their first win.
Andrea Colpani put the Silvio Berlusconi-owned side ahead just after the half-hour but the lead only lasted four minutes before Beto levelled for Udinese.
Monza were looking good for their first point of the season until 19-year-old defender Destiny Udogie, on loan from Tottenham, knocked in the winner 12 minutes from time.
On Saturday, Juventus host Roma, who have won two out of two, while Bologna travel to AC Milan. Napoli can also go three wins from three when they travel to Fiorentina on Sunday.