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Dzeko scored with the last touch of the game - contorting his body to somehow divert Stephan El Shaarawy's cross goalward - to rescue the win for the Giallorossi, on a night where they struggled for fluency at the Stadio Benito Stirpe.
Nevertheless, the win means Eusebio Di Francesco's side remain firmly in the race for the top-four, with other rivals still to play later in the weekend.
Against one of the league's struggling sides, Roma contrived to go behind after just five minutes - as Camillo Ciani took advantage of some midfield indecision to fire home from long range.
But, in just a 72-second span midway through the half the Giallorossi turned things around, as first Dzeko - pouncing on some hesitation in the box to fire home - and then Lorenzo Pellegrini - tapping in after El Shaarawy's shot was parried across the goalmouth - put the visitors in control.
But another goal would not be forthcoming until Frosinone substitute Andrea Pinamonti swept in with 10 minutes remaining, setting up a frantic finish.
Only a great save from Robin Olsen denied another substitute, Marcelo Trotta, a potential winner. But then it was Daniele De Rossi, captaining his hometown club for the 200th time on the night, who split the defence with one final, masterful ball; allowing El Shaarawy to get to the byline and cross for Dzeko.
Roma are next in action the following Saturday, as they meet Lazio in the Derby della Capitale.
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