Lazio humbled AC Milan with a superb 4-0 home victory in Serie A on Tuesday, extending the champions' winless run to five games in all competitions.

Sergej Milinkovic-Savic, Mattia Zaccagni, Luis Alberto and Felipe Anderson were all on target to send Maurizio Sarri's side into the third place, one point behind Milan and 13 off the leaders Napoli.

Milan continued their recent poor form after they were hammered 3-0 by rivals Inter Milan to lose the Italian Supercup last Wednesday, and crashed out of the Coppa Italia in the last 16 against 10-man Torino the week before.

"There are many things not working (at Milan) at the moment," coach Stefano Pioli said.

"There's mentality, tactical issues because we conceded on some situations that we certainly should have read differently."

Milinkovic-Savic fired Lazio in front after four minutes with a low shot into the bottom-left corner after Zaccagni set him up with a cross into the middle of the box.

Anderson could have added a second goal for Lazio in the 36th minute but the pass he received from Pedro just in front goal was slightly too powerful for the Brazilian to convert.

However, Zaccagni doubled Lazio's lead two minutes later, after midfielder Adam Marusic hit the post from the edge of the six-yard box for the Italian to follow up with a tap-in from close range.

Milan had a chance to pull one back four minutes into the second half, but midfielder Ismael Bennacer sent his powerful free kick inches wide of the right post.

Lazio, who were without injured striker Ciro Immobile, who has seven goals in Serie A this season, made it 3-0 from the spot through Luis Alberto, after they were awarded a penalty for a foul by Pierre Kalulu on Spaniard Pedro.

Anderson wrapped up the scoring for Lazio in the 75th minute, calmly converting Luis Alberto's precise cross from the edge the box for his sixth Serie A goal this season, and fourth in consecutive games in all competitions.

Joshua Kimmich scored Bayern's leveller as they started 2023 with consecutive draws

In Germany's Bundesliga, Bayern Munich's Joshua Kimmich thundered in a 90th minute equaliser to rescue a 1-1 draw against Cologne on Tuesday, staying four points clear at the top.

The German champions, chasing a record-extending 11th league crown, had possession but were far less effective than their opponents who looked to be snatching the three points courtesy of Ellyes Skhiri's fourth minute volley at the far post.

But Kimmich scored with a long-range effort to lift leaders Bayern, who have now drawn their last two league matches, to 36 points.

"We had to change things after the second half and we dominated after the break. Two points from the last two matches is too little for us," said Bayern coach Julian Nagelsmann.

The Bavarians had also drawn 1-1 against RB Leipzig last week.

RB Leipzig, 6-1 winners against Schalke 04, are in second place on 32. Eintracht Frankfurt, third on 30, take on Freiburg on Wednesday.