Chris Smalling scored the only goal of the game in front of over 60,000 in the Italian capital, deciding the game just as it threatened to become a somewhat nervy affair.
Jose Mourinho's side had certainly had their chances throughout but, with the final 25 minutes approaching, the newly-promoted visitors were undoubtedly growing in confidence and threat.
Smalling dealt with that, however; heading home from Lorenzo Pellegrini's corner at the back post to ensure the winning start continued.
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In truth there were plenty of chances at both ends, with Cyril Dessers, Charles Pickel and substitute Cristian Buonaiuto all going close for Cremo - who gave their travelling supporters a lot to be positive about over the rest of the season.
Yet the better chances nevertheless fell to Roma, with Lorenzo Pellegrini forcing Ionut Radu into one spectacular save, before Paulo Dybala narrowly fired the rebound wide.
Other chances came and went, until Smalling's moment of inspiration.
The Giallorossi are back in action on Saturday - they travel to Turin to take on Juventus.
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