Ancelotti got off to a winning start in Saturday evening's clash at the Stadio Olimpico, however, as his Napoli side saw off Lazio through goals from Arkadiusz Milik and Lorenzo Insigne either side of half time.
In a meeting between last term's second and fifth-placed sides, Insigne had the first shooting opportunity following some good build-up play with Piotr Zielinski, only to shoot over the crossbar.
The Polish midfielder then slotted wide, and moments later Lazio were in front as Ciro Immobile took three players out of the game with a single touch, before tucking the ball out of Orestis Karnezis's reach.
Napoli responded well, coming close through an Insigne shot and then seeing Zielinski hit the crossbar with his deflected effort.
A disallowed Milik goal followed, as well as a fine Thomas Strakosha save to deny the striker, but Napoli were on level terms before the break thanks to a tap-in from the same player after Strakosha parried a shot.
With just short of an hour played the visiting side took the lead for the first time, with Insigne curling the ball into the top corner of the net from eight yards for what proved to be the winner.
Karnezis was called into action again to produce a fingertip save, while Immobile was twice thwarted when in a promising position.
There was so nearly a late twist in the Italian capital as Francesco Acerbi picked out the post with his attempt in the closing stages, but in the end the Biancocelesti could not muster a second goal.
LAZIO (3-5-2): Strakosha; Luiz Felipe (Bastos 46'), Acerbi, Radu; Marusic, Parolo (Cataldi 88'), Badelj (Correa 68'), Milinkovic-Savic, Caceres; Luis Alberto, Immobile
NAPOLI (4-3-3): Karnezis; Hysaj, Albiol, Koulibaly, Mario Rui; Zielinski (Rog 75'), Allan, Hamsik (Diawara 70'); Insigne (Mertens 76'), Milik, Callejon