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The hosts hit the bar in both halves - courtesy of Adrien Tameze and Federico Dimarco - but also had the frame of the goal to thank late on, as Leonardo Spinazzola's long-range half-volley crashed down off the crossbar and out.
While Antonio Mirante got a crucial touch to flick Tameze's first half strike away from the target his opposite number, Marco Silvestri, was also often busy - with a diving save from Lorenzo Pellegrini frustrating the Giallorossi captain midway through the second half.
Henrikh Mkhitaryan and Pedro - making his debut for the club - also both had great first half chances courtesy of Spinazzola, although both attackers dragged their first-time shots wide.
As time wore on the hosts grew in confidence and threat, but Mirante never looked in serious danger of conceding - especially after Davide Faraoni's marauding run ended with him dragging a cross harmlessly across goal.
Paulo Fonseca's side are back in action next weekend - they host Juventus in their first home game of the season at the Stadio Olimpico on Sunday.
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