The Giallorossi fell to a 3-0 half-time deficit, as Francesco Caputo and Filip Djuricic punished the travelling side on the counter-attack.
Edin Dzeko's 100th goal for the club gave Paulo Fonseca's side a way back into the match - and Jordan Veretout cut the deficit further from the penalty spot, even after Lorenzo Pellegrini had been sent off.
But Jeremie Boga finished off a fine solo run just moments after to effectively kill off the contest with 15 minutes remaining.
The Giallorossi are back in action on Friday - as Bologna visit the Stadio Olimpico.
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