The Argentinian held his nerve from the penalty spot to give the Nerazzurri a 3-1 lead in the 67th minute and led in the line impressively in the continued absence of exiled star striker Mauro Icardi.
Icardi was stripped of the captaincy in February and has not featured for Spalleti’s side since, amid mounting speculation about his future at the San Siro.
Goals from Matias Vecino and Stefan De Vrij had given Inter the lead, before Tiemoue Bakayoko hit back for the Rossoneri.
Lautaro’s spot-kick extended the lead, but Mateo Musacchio gave Gennaro Gattuso’s side hope with 20 minutes remaining.
However, Inter held on to climb to third in the Serie A, overtaking Mlian, a result which left Spalletti purring over the 21-year-old front man.
“Lautaro is powerful, has technique, confidence,” Spalletti said. “You just need to look him in the eyes and you can tell he can take on everything.
“We’ve found a young striker who can sort a lot of things out for us.
“We need to say well done to Lautaro for the penalty, well done to Perisic for the runs, well done to everyone for all you did. Bravo, Bravo to everyone in that dressing room.
“I also say Bravo to the fans, because they let the team know that they were behind us even in moments of difficulty.”