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Diawara scored in the final few minutes to ultimately decide a fraught match at the Artemio Franchi - with VAR employed to confirm that substitute Rick Karsdorp was onside as he squared the ball into the box for the midfielder.
Leonardo Spinazzola had earlier scored at both ends, as both sides seemed to struggle to create - or take - clear-cut chances.
Both goalkeepers had their moments during the 90 minutes in Tuscany, with Bartomir Dragowski in the Fiorentina goal particularly active on occasions - as he denied Lorenzo Pellegrini and Borja Mayoral at key moments in each half.
He had no answer for Spinazzola's breakthrough minutes into the second half, however, as the full-back briefly turned into a striker with a pinpoint volley on the turn that found the bottom corner.
Moments later he was altogether less fortunate, however, as he turned into his own net to erase the advantage he had just created.
The game thus seemed to be heading for a draw, until Diawara ghosted between the Fiorentina defence to finish off Karsdorp's cross. Initially the flag went up - but a VAR check eventually ensured the goal stood, and with it a vital away victory was secured.
The Giallorossi are back in action on Sunday, as they host Genoa.
FIORENTINA 1-2 ROMA
SCORERS: Spinazzola (o.g. 60'); Spinazzola (49'), Diawara (90')
FIORENTINA (3-5-1-1): Dragowski; Milenkovic, Pezzella, Martinez Quarta; Venuti, Amrabat, Pulgar (Caceres), Castrovilli (Kokorin), Igor (Biraghi); Ribery (Borja Valero); Vlahovic
Unused subs: Terracciano, Rosati, Olivera, Malcuit, Barreca, Montiel, Callejon, Eysseric
ROMA (3-4-2-1): Pau Lopez; Kumbulla (Smalling), Cristante, Mancini; Peres (Karsdorp), Veretout (Pedro), Diawara, Spinazzola; Mkhitaryan (El Shaarawy), Pellegrini; Mayoral
Unused subs: Mirante, Fuzato, Villar, Fazio, Pastore, Perez
Imperium Partners
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