Authorities are currently investigating the sightings
Radja Nainggolan opened the scoring in the 40th minute, then Dzeko finished from close range in the 77th to raise his league-leading tally to 18 goals.
Roma moved back ahead of Napoli into second place, four points behind Italian leader Juventus, which visits Cagliari later.
Napoli beat Genoa 2-0 on Friday. It was only the sixth win in 13 away matches for Roma, which has won all 11 of its home fixtures.
Shortly after the quarter-hour mark, Mohamed Salah was pushed down inside the area to set up Dzeko's penalty. The Bosnia and Herzegovina international hesitated to see which way goalkeeper Alex Cordaz went but then kicked a low shot wide of the goal in the same direction.
It was Dzeko's second miss from the penalty spot this season - most in Serie A. "It happens. It's nothing serious but I won't be taking the next one," Dzeko said.
Still, Roma controlled throughout against a Calabrian squad playing in the top flight for the first time in its 107-year history. The Giallorossi went ahead when Nainggolan scored with a low, angled shot across the area into the far corner. It was his sixth of the season, already matching his career best set last term with 14 matches still to play.
In the 53rd, Nainggolan set up Dzeko, whose shot was slightly deflected off the bar. It was the sixth time Dzeko has hit the goal frame this season - also more than any other player in the league.
A minute later, Roma wasted another chance when a header from defender Federico Fazio hit the post following a corner with Cordaz beaten.
Dzeko finally hit the target after a nice setup from Salah left him with plenty of room to find the target.
Authorities are currently investigating the sightings
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