Joaquin Correa scored twice as Lazio enhanced their chances of qualifying for the UEFA Champions League and left Milan out of the top four with a 3-0 win at fortress Stadio Olimpico.
Correa scored after only 77 seconds and struck again in the second half to seal a deserved victory for Lazio in head coach Simone Inzaghi's first game back on the touchline since recovering from the coronavirus.
The prolific Ciro Immobile rubbed salt into the wounds with a late third as Milan were toothless in defeat to Stefano Pioli's former club and slipped to fifth in the Serie A table, level on points with Napoli and Juventus.
Lazio are five points adrift of the Rossoneri, after securing a 10th successive home victory in the top flight, and they have a game in hand in what is shaping up to be a tense battle for Champions League qualification.
Hakan Calhanoglu could have got Milan off to a dream start but the Turkey playmaker's strike was palmed away by Pepe Reina.
It was the Biancocelesti who were in front in the second minute courtesy of a cool finish from Correa, who exchanged passes with Immobile before nonchalantly rounding Gianluigi Donnarumma and tapping into an empty net.
Manuel Lazzari thought he had doubled Lazio's lead late in the first half, but a VAR check showed he was marginally offside before Mario Mandzukic failed to beat Reina when he was presented with an opportunity just prior to the break.
Lazio had their second goal six minutes into the second half, when Correa beat Fikayo Tomori before drilling into the roof of the net with his right foot and referee Daniele Orsato saw nothing untoward when he checked the pitch-side monitor for a potential foul on Calhanoglu.
Donnarumma produced a superb fingertip save to deny Correa a hat-trick as Milan struggled to live with Lazio's passing, movement and pace.
A deft Immobile lob came back off the post before the striker lashed home his 23rd goal of the season off the base of the post with a clinical right-foot finish three minutes from time.
Franck Kessie headed against the crossbar in the closing stages to cap a miserable night for Milan.