Roma thumped the Viola 4-2, with midfielder Gerson scoring twice.
Di Francesco said, “I've been following Gerson's progress since I was at Sassuolo and he suits my style of football very well. I have to say, though, Edin Dzeko impressed me more than anyone today. In the final minutes, he tracked back to win possession and stop a Fiorentina attack. That is teamwork.
“At the start, the players struggled a little to get a hang of my tactics, but they have embraced my ideas now and we are seeing the fruits of that labour.
“I also share this wonderful record of away wins with Spalletti and hope that I can create a new record on my own too."
He added: "I was afraid of this match, because after the win over Chelsea I feared we'd see a team that was sated, but instead it was a good response from the lads. They are still hungry."