Both teams' openers featured two managers coaching in the competition for the first time, with former Milan defender Ignazio Abate in the home dugout.
Amorim’s men started brightly and Cisse almost opened the scoring inside two minutes, but the 19-year-old attacking midfielder hit the side-netting from a tight angle after meeting Ruben Loftus-Cheek’s low cross.
That was Milan’s best chance of the opening quarter, as they continued to dominate possession but failed to test Torino goalkeeper Diego Mascardi, another 19-year-old making his SA debut.
Mascardi made his first save just before the half-hour mark, denying the lively Samuel Chukwueze with his legs after the wing-back slalomed into the penalty area.
It was the only shot on target by either side in a first half that lacked attacking quality, with Torino keeping Milan’s €74million club-record signing Goncalo Ramos quiet in his first outing for I Rossoneri.
Amorim was first to blink 11 minutes into the second half, as he brought on experienced midfielders Luka Modrić and Adrien Rabiot for Loftus-Cheek and Ardon Jashari.
Torino had struggled to threaten, but Giovanni Simeone nearly followed up his winner in last Saturday’s 1-0 Coppa Italia victory over Carrarese when his fierce shot was blocked at point-blank range.
However, Milan finally made their dominance pay in the 64th minute, when Rabiot crossed for Cisse and the teenager took a touch before guiding an excellent finish past Mascardi.
Rabiot turned from provider to goalscorer three minutes later, as he sent a close-range volley high into the net from Chukwueze’s cross to score against Torino for the third successive Serie A game.
Abate made a triple substitution and one of the replacements, Alieu Njie, fired against the post as the hosts searched for a response, before debutant Pietro Comuzzo volleyed over.
Another substitute, Che Adams, pulled one back in stoppage time as he contorted his body to meet a free-kick with an incredible first-time volley into the top corner.
However, Torino’s late burst came too little, too late, as they suffered their first home league defeat since February 15.
In contrast, Amorim is the first foreign coach to win their first season opener in charge of Milan since 2009, giving I Rossoneri the perfect start to the campaign.
Flashscore Man of the Match: Samuel Chukwueze (AC Milan)