The Germany international's volley at the start of the second half ultimately proved decisive, in spite of a spirited late fightback from Massmiliano Allegri's men
The visitors fell behind to a deflected effort from Hernanes midway through the first half before Antonio Candreva doubled the Biancocelesti's advantage with a stunning strike just before the interval.
Miroslav Klose made it 3-0 early in the second half and although Nigel de Jong and Stephan El Shaarawy dragged Milan back into the game after the introduction of the fit-again Alexandre Pato, last season's runner-up was unable to complete what would have been a remarkable comeback.
Even though the visiting side had made its worst start to a Serie A campaign in 80 years, the under-pressure Massimiliano Allegri looked like he did not have a care in the world before kick-off.
The Rossoneri coach was given very little cause for concern during an opening quarter in which Milan coped comfortably with what little Lazio had to offer going forward, while at the same time threatening sporadically themselves.
However, when it comes to struggling sides, anything that can go wrong, usually does go wrong, and so it was that the visitors fell behind 25 minutes in when Hernanes twisted and turned his way past Daniele Bonera before unleashing a speculative effort which struck the defender’s outstretched leg and looped up and over the stranded Marco Amelia.
Fortune frowned on Milan again just moments later when El Shaarawy, having latched onto a through-ball from Antonio Nocerino, fired the ball through the legs of Albano Bizzarri only to see Andre Dias seemingly come from nowhere to clear off the line.
It was hit with another devastating psychological blow just before the break when Candreva unleashed a long-range drive that seemed to swerve in several different directions on its way past an understandably bemused Amelia.
Despite the benefit of 15 minutes’ respite, Milan still appeared punch drunk at the start of the second half. It would be difficult to offer another credible explanation for the way in which they defended Lazio’s third goal, with right-back Ignazio Abate missing in action and a dazed and confused Daniele Bonera staggering about the box as Klose clinically volleyed home Candreva’s measured cross from the right wing.
That looked like the knockout blow but Milan kept swinging and their fighting spirit was rewarded with a goal from De Jong, who did well to get his toe on Urby Emanuelson’s low, in-swinging free kick.
Suddenly it was the hosts who looked fragile - both mentally and defensively - and Milan set up a fascinating finale when El Shaarawy cut in from the left with just over 10 minutes to go and curled the ball into the bottom corner.
Milan poured forward in search of an equaliser but to no avail, meaning it remains 12th in the standings. Lazio also stay where they are, but the third-placed Biancocelesti are now just one point behind second-placed Napoli.
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