At a raucous Stadio Olimpico, Sarri's side ran out 3-2 winners to inflict a second defeat on the Special One in his new job.
Sergej Milinkovic-Savic gave Lazio an early lead before Pedro, who played under Mourinho at Chelsea, made it 2-0.
Roma defender Roger Ibanez pulled one back back just before half time but Felipe Anderson's goal restored the two-goal lead for Sarri's side.
Jordan Veretout's 69th-minute penalty made it a nervous finish but Lazio kept hold of their lead to claim the derby win.
And what does one do when you've won the Derby della Capitale? Celebrate with the club's mascot of course.
Lazio's mascot is an eagle named Olympia and Sarri held her aloft as he saluted the Curva Nord crowd after the final whistle - and it appears the two are already firm friends.
Sarri, who took over as Lazio boss in June, said: "Olympia sleeps close to my room at the Formello training ground, so I hear her sometimes.
"I will admit, it was emotionally one of the most exhilarating matches of my career.
"I didn't expect the derby to give you this adrenaline rush and satisfaction at winning. This is real football, it's not a PlayStation game.
"I saw seven or eight situations that I really liked, but we cannot clone one team and make it work elsewhere."
In contrast, Mourinho channelled his inner-Phil Brown after the match as he gave his players a dressing down on the pitch.
And after the game he had time to complain about VAR.
"Unfortunately, a fantastic game was ruined by the referee and VAR, who were not at the right level for this match," the Mourinho told DAZN.
"The second goal could've been 1-1, it went to 2-0. The [lack of a] second yellow for Lucas Leiva was important too. I think my team was the best on the field today.
"We dominated, we gave Lazio huge problems, they controlled the final minutes the way they wanted to, and because the referee allowed them to do so."