Only Silvio Piola, who scored most of his 274 goals for Roma's bitter rivals Lazio, is above him, 48 in front.
"Now my goal is to exceed Piola," the 36-year-old said on www.gazzetta.it.
The victory moved Roma level on points with fifth-placed Inter Milan and boost hopes of European qualification.
"I'm happy with the win," Totti added. "I think it was the wonderful evening we all wanted. We were so many points behind Inter, now we are level on points."
Roma boss Aurelio Andreazzoli, appointed until the end of the season following the departure last month of Zdenek Zeman, praised Totti's influence.
"Totti? It's always much easier with him around, he makes difficult things look easy," he said on the club website.
Totti also wants Andreazzoli to remain in charge beyond the end of the season.
"Totti has said that if we continue like this he'd like me to continue as coach next season?" added the boss.
"The captain buying into it is very important, of course, but he's biased: he's my buddy."