The former Manchester City centre-forward struck in the 39th and 66th minutes following his goal in Tuesday's 5-2 semi-final, first leg loss.
Dzeko fed off Aleksandar Kolarov, another ex-City man, who provided the perfect cross for his first.
In the second half he thanked Radja Nainggolan for the through ball that allowed him to shake off a couple of Chievo players and fire home.
Dzeko later hit the cross bar with a stinging drive from 25 yards.
Roma host Liverpool in the second leg of their European showdown on Wednesday.
They also hit the target through Patrik Sckick and Stephan El Shaarawy.
Roma had Juan Jesus sent off for a professional foul in the 56th minute.
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The visitors managed an 88th minute consolation goal through Roberto Inglese.
Roma goalkeeper Alisson had earlier saved a penalty from the Chievo striker.
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With the Liverpool re-match in mind, Roma Eusebio Di Francesco made four changes from the side hammered on Merseyside.
Konstantinos Manolas, Alessandro Florenzi and Cengiz Under all dropped to the bench.
Kevin Strootman missed out entirely and is a doubt for the return leg.
Diego Perotti, who scored from the penalty spot to bring the Italians their second away goal on Tuesday, was another absentee from the squad.
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