The 2013 winners had plenty of opportunities to claim an advantage, including Ciro Immobile’s delicate lob in the second half, but Gennaro Gattuso’s side will return to the San Siro the happier of the teams.
“The regret is that we didn’t manage to score,” Lazio coach Simone Inzaghi told Rai Sport.
“We were only missing a goal. But the lads put in a great performance, were always very focused against Milan, who are the form team in Serie A right now.”
After a poor opening quarter of an hour as both teams failed to assert any control, the ball broke to Lucas Paqueta in the home side’s box.
Tiemoue Bakayoko’s deflected shot fell to Paqueta but his shot was weak in threatening Thomas Strakosha.
The capital city side dominated the remainder of the first half with plenty of chances which they should have taken.
Patric, Immobile and Sergej Milinkovic-Savic all saw tame efforts from inside the box glance past Gianluigi Donnarumma’s right-hand post.
The hosts had a penalty shout turned down just after the hour mark.
Immobile was pushed to the ground by Alessio Romagnoli as he cushioned the ball with a header, but he was judged to be offside by the assistant referee.
Serbian Milinkovic-Savic finally had a shot on target on 66 minutes as his deflected effort forced Donnarumma to dive to his left.
The best chance of the final 45 fell to Immobile with 10 minutes to play.
He found himself in space one-on-one against youngster Donnarumma, but his audacious attempted chip hit the post and rolled out for a goal kick.
He was immediately substituted for Felipe Caicedo by Inzaghi, whose first touch was to earn a wasted corner.
The visitors had a chance to secure an away-goal advantage with three minutes to go as Fabio Borini’s impressive overhead-kick cross found Krzysztof Piatek, but his header sailed over the bar.