The Egypt international made it 2-0 soon after before it became Dzeko's turn to shine, as the Bosnian forward made it 3-0 inside the first 18 minutes with a close-range finish.
18-year-old Christian D'Urso also managed to get himself on the scoresheet, before Dzeko added another three goals just before the half-time whistle.
Between those strikes, both Diego Perotti and Vasilis Torosidis found the back of the net to make it 9-0 at half-time.
Then came the changes, as a completely eleven came out for the second half. It only took ten minutes for the new boys to add to the already emphatic scoreline, as Juan Manuel Iturbe won and converted a penalty.
Federico Ricci, on loan at Crotone last season, then showed his cutting edge in front of goal as he slotted home after good work from Iturbe, before Gerson marked his first appearance in a Roma shirt with a goal after curling a beautiful effort home from 20 yards.
By then, the floodgates were well and truly open as youngsters Ezequiel Ponce and then Lorenzo Di Livio both hit the target from close range. Ricci then added to his tally, bringing the scoreline to 15-0 with just minutes remaining.
In the end it would be Iturbe who finished off the scoring, as he raised one of the loudest cheers of the afternoon with a thunderbolt from 25 yards that left the goalkeeper with no chance.
Roma's final game in Pinzolo takes place on Sunday, as Russian side Terek Grozny come to town.
