Lazio shot into Serie A's Champions League places on Tuesday after hammering AC Milan 4-0 to leave the champions' title defence hanging by a thread. 

Lazio breezed up to third on goal difference, ahead of Inter Milan and local rivals Roma, and a point behind second-place AC Milan, who gave a disastrous display at the Stadio Olimpico in Rome.

Sergej Milinkovic-Savic put Lazio ahead after three minutes with a first-time finish. By the time Mattia Zaccagni bundled in the hosts' 38th-minute second they could have already been up by three.

Luis Alberto ended the match as a contest by smashing home a penalty midway through the second half his beautifully disguised pass set up Felipe Anderson to roll in a deserved fourth in the 75th minute.

Milan are 12 points behind runaway league leaders Napoli at the season's halfway point and have lost their aura as the country's top team.

Three league matches without a win have allowed Napoli to skip away to a commanding lead, while Milan have four teams breathing down their neck for second place.

Lazio are one of three sides trailing them by a single point while in-form Atalanta are a further two points back in sixth, as the race for the top four hots up.

Maurizio Sarri's Lazio team were missing star striker Ciro Immobile but had no problem getting at a Milan defence which has conceded 12 goals in their last five matches in all competitions, losing three and drawing two.

Coach Stefano Pioli lost France's Theo Hernandez ahead of the match and starting centre-back Fikayo Tomori to injury in the 24th minute before full-back Davide Calabria hobble off in stoppage time.

Those were more blows for a team who have the Milan derby coming up in less than a fortnight -- against the  side who gave them a lesson in the Super Cup last week -- and  a Champions League tie with Tottenham on the horizon.