With Chelsea leading 2-1 in the second half, Dzeko's goals turned the match on its head and his first – a sublime volley from a Federico Fazio cross – will live long in the memory.
The 31-year-old headed Roma into the lead six minutes later, only to see Eden Hazard score an equaliser for Chelsea with 15 minutes left.
Di Francesco praised his in-form striker, as well as the rest of his team, telling Premium Sport : "Dzeko was born to score these goals. He has been criticised very often but tonight he made the difference.
"Even when we were losing, I saw a team who interpreted what I had asked and did well. From the point of view of performance I'm happy.
"It is regrettable that when you play so well but you can't bring home the result you want."
Dzeko said that Roma, by pushing Chelsea to the brink on their own turf, proved how far Italian football has come in recent years.
"It's a splendid night for us," he told Mediaset Premium after taking his personal goal tally to nine in his last seven games for the club.
"A point is good, but we could've won. We played an incredible match, all together from the first minute. It's a shame that we conceded three goals, as that means we have more work to do, but Chelsea are strong and converted all their chances.
"We had the right mentality. We played as if we were the home side from the opening minute. I already said yesterday that Italian football has improved a lot and we saw that tonight too.
"When I was at Manchester City, I never scored against Chelsea, but I made up for that."