Claudio Ranieri had won three derby games, but it was the first as Coach for Vincenzo Montella.
"Since Vincenzo arrived, the mentality of the team has changed. You can see the hunger to win," said Totti.
"I am happy to dedicate this victory to the Sensi family, who deserve it for all they have done and the passion they put into the club. We must all thank the President.
"I also dedicate it to my wife, Ilary, as we have now been together for nine years."