Ante Rebic scored with 15 minutes remaining to break the deadlock at an empty San Siro, with both sides visibly tiring in the stifling afternoon heat of northern Italy.
Hakan Calhanoglu then scored the clincher from the penalty spot in the final few minutes, after Chris Smalling was adjudged to have fouled Theo Hernandez.
Paulo Fonseca's side perhaps edged the match in its opening stages, with Edin Dzeko failing to convert perhaps the best chance of the first half - as he headed wide from close range.
It remained an even contest well into the second stanza, at least until Rebic continued his fine recent run of goalscoring form as he lashed home at the second attempt from inside the box.
The Giallorossi are back in action on Thursday evening at the Stadio Olimpico, with Udinese the visitors.
They then travel to face Napoli on Sunday.
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