The Rossoneri were level ten minutes later from Robinho's close-range volley.
In a frantic opening spell, Milan found themselves ahead minutes later when Clarence Seedorf rounded Federico Marchetti before firing in.
Robinho could have added a third soon after, but the Brazilian hit the sidenetting after taking the ball around the keeper.
Cisse had his head in his hands before the break as he smashed the ball wide at the back post when he was unmarked.
In a scrappy second half, Stephan El Shaarawy almost put the game beyond Lazio's reach just after the hour, but he could only blaze over from six yards out.
Substitute Miroslav Klose nearly had a dream introduction for Lazio after 65 minutes when his header was saved by Marco Amelia.
Zlatan Ibrahimovic came off the substitutes' bench to liven up Milan's front line, and the Swede killed off the game with five minutes to go when he collected Emanuelson's pass before cooly slotting past Marchetti.
Massimiliano Allegri's side will now face Juventus for a place in the final.