Vladimir Petkovic's men fell behind to an early Erik Lamela goal, but fought back with goals from the veteran forward, Antonio Candreva and Stefano Mauri to claim a narrow victory in a thrilling contest.
“This was a very important victory for us, the club and the fans,” the Germany international told reporters.
“It was difficult to play on this pitch, but we put in a great performance. Am I a decisive man in the derby? No, the important thing is that the team does well and wins.
"I am not interested in who scores or not, just that we got the points."
Having suffered from a difficult start at his current club, Candreva was particularly delighted over having netted the all-important equaliser by converting a free-kick.
“It was a curious game,” he commented. “We managed to get it back on track before half-time, but derbies are always one-off occasions.
"I have dreamed of this goal since the moment I arrived here."
Lazio now sit in fifth place in Serie A, nine points behind current leaders Juventus.