The victory also earns Lazio a place in the Europa League group stage for next season.
Two AC Milan players were subjected to racially insulting chants before and during last Wednesday's match at San Siro.
After knocking out Inter Milan in the quarter-finals, Lazio continues their giant killing run in the Italian Cup by taking out AC Milan to reach the final.
Lazio suffered their 3rd straight defeat in all competitions.
Some 40 people are involved in the clashes near the Colosseum which is broken up by police in riot gear.
Felipe Caicedo forces a penalty just before the break and converts from the spot for his second goal in.
Lazio lost the Coppa Italia semi-final to Milan on penalties last season.
Juventus have 59 points out of a possible 63, while 2nd-placed Napoli are on 48 after their 0-0 draw at AC Milan.
Lazio are sixth, two points outside the top four places which earn a place in next season's Champions League.
Napoli, with 47 points, open up a 7-point gap between themselves and 3rd-placed Inter Milan.
The 23-year-old scored his second of the season after 12 minutes when Joaquin Correa's angled drive was cleared by Cagliari keeper Alessio Cragno into Milinkovic-Savic's path, with the Serb finishing off.
Atalanta, now 6th equal on points with Roma and Sassuolo, move 1 point behind Lazio, in 5th, but without a win in their last 5 league games.
Arsenal's 0-0 draw against Sporting Lisbon and Chelsea's 1-0 win over BATE Borisov put them in the Europa League's round of 32, but Marseille's loss to Lazio knocked them out of the tournament.
Ciro Immobile scored two of Lazio's goals in their 4-1 win over SPAL.
Marseille fans have been banned from buying tickets for next week's Europa League match against Lazio.
Inter have clearly got over their shaky start to the season, which included shock defeats to Sassuolo and Parma.
Federico Fazio allowed Lazio to score a goal, but also scored the third goal in Roma's 3-1 Derby della Capitale victory.
Marseille were drawn with Lazio, Apollon Limassol, and Eintracht Frankfurt in their Europa League group.
Juventus have six points from two games after a somewhat fortunate win, but Ronaldo is still waiting for his first goal since his move from Real Madrid.
Controversial sexist leaflets attributed to Lazio ultras circulated before the team's opening Serie A game.
Final-day, winner-takes-all league matches are usually matches that live long in the memories of all who watch them.
Inter had to win in order to take third place from Lazio who had a superior head-to-head record and needed just to draw.
Lazio's 2-2 draw against Crotone means that they will now have to play against Inter Milan in a winner-takes-all match for the last Champions League spot.
Having played to a 0-0 draw in their first leg at the San Siro one month ago, Lazio and AC Milan produced a repeat performance in Wednesday's return at a freezing Stadio Olimpico despite creating plenty of chances.
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