Now on 105 for the Giallorossi - fifth on his own in the overall standings - Dzeko surpassed the Argentina-born Pedro Manfredini to take the record on his own.
The Bosnia & Herzegovina striker headed home in first half injury time, as Roma beat Hellas Verona 2-1 at the Olimpico.
He needs one more goal to draw level with Rodolfo Volk for fourth all-time on the club's goalscoring charts.
Amedeo Amadei, Roberto Pruzzo and Francesco Totti are the other men still above Dzeko.
Congratulations Edin!
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