Balotelli, Taarabt and Pazzini were on target for Milan as they climbed up the table to keep their hopes of Europa League football alive
Adel Taarabt and Giampaolo Pazzini joined Balotelli on the scoresheet to settle the contest at San Siro and pile more misery on the relegation-threatened visitors.
The win marks Milan's fifth straight Serie A victory and keeps their hopes of Europa League qualification alive, as well as easing the pressure on coach Clarence Seedorf amid rumours that he will be replaced at the end of the season.
Balotelli had been a doubt to start after leaving the warm-up early with an apparent thigh problem, but showed no ill-effects as his 30th goal for the club ensured they led at the break.
Milan continued to dominate after the break, and Taarabt combined with Balotelli for the second six minutes after the restart.
Substitute Pazzini then rounded off matters late on when he latched onto a Balotelli throughball before coolly finishing past Francesco Bardi.
Seedorf's side move up to seventh with the win, five points behind fifth-placed rivals Inter, while Domenico Di Carlo's Livorno are now 19th, three points adrift of safety with four games remaining.
After a somewhat tentative opening, Taarabt almost sparked the game into life with a rasping 25-yard drive that cleared the crossbar in the 11th minute.
Soon after, Milan went even closer. Captain Riccardo Montolivo played a hopeful free-kick from the halfway line into the area, where Adil Rami looped a header over Livorno goalkeeper Bardi but was denied by the bar.
The hosts continued to create the better opportunities and Kaka almost broke the deadlock with a fierce first-time strike from the left of the box that cleared the far post.
Livorno had largely been chasing shadows for the opening half hour, yet the visitors had claims for a penalty when Djamel Mesbah was tripped after outpacing Ignazio Abate, only for referee Massimiliano Irrati to correctly judge the infringement to have occurred just outside the box.
And having survived that scare, Milan deservedly moved ahead two minutes before the interval.
Kevin Constant's superb whipped cross from the left was met with a glancing header by Balotelli, who marked his appearance milestone with his 14th Serie A goal of the campaign.
Milan essentially ensured the three points shortly after the restart. Taarabt played a superb one-two with Balotelli before keeping his composure to slot past Bardi from eight yards.
Just after the hour mark, Kaka had the chance to extend the hosts' advantage but the Brazilian blazed over from close range.
However, Pazzini, who came on for Kaka with 15 minutes remaining, got in on the act when he side-footed beyond Bardi after cleverly timing his run onto Balotelli's pass.
Milan have now won five consecutive league games for the first time since 2011, and their late challenge for European football continues.