Despite having the vast share of possession and a catalogue of chances, Massimiliano Allegri's men could not break down a stubborn Roman wall of defiance.
Lazio were the first to press and Cristian Ledesma's shot inside the opening minutes almost caught out Christian Abbiati in the Milan goal.
The Argentine midfielder cut in from the left-hand side and hit a stinging right-footed effort.
It looked to be easy enough for Abbiati until it took a wicked deflection off Daniele Bonera which forced the Milan goalkeeper into a smart save to his right.
Milan should have gone ahead after 20 minutes.
But instead of opening the scoring he blazed a left-footed volley over the crossbar.
Indeed it was a Lazio player who very nearly got on the scoresheet first, but for the wrong team.
Flamini's cross towards the left was met by Zlatan Ibrahimovic's header; the Swede intended to head back across goal but Biava got in the way and almost guided the ball inside the near post.
The best chance of the half fell to Milan's Urby Emanuelson, who has only recently joined from Ajax.
The midfielder was found inside the penalty by Ibrahimovic's clever pass but he could only blaze an ugly drive over the crossbar when it seemed easier to score.
Milan had three chances in as many minutes at the start of the second period.
The first opportunity saw Ibrahimovic denied by both posts after Alexandre Pato had robbed Biava of the ball.
The Sweden striker moved inside from his position on the left and shot from 20 yards only to see the effort beat Muslera in the Lazio goal then strike both posts before the goalkeeper could recover.
Flamini was the next to threaten but after being released by Thiago Silva his shot across goal was easily saved.
Then Ibrahimovic attempted to curl an effort from the left of the penalty area towards the far post but even he could not make the ball curl enough.
Robinho nearly got his name on the scoresheet after 64 minutes. The ball reached the Brazilian on the right of the penalty area and despite beating Muslera with his shot Stephan Lichtsteiner was on hand to clear off the line.
That was as good as it got for the home side as Lazio continued to strangle the game and Milan were left to rue their many chances.
AC Milan will next travel to Genoa on Sunday while Lazio entertain Chievo.
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