The win, their 15th in 20 league games this season, left second-placed Napoli six points behind leaders Juventus - who host bottom club Chievo on Monday evening (Tuesday morning AEDT) - while Lazio dropped out of the UEFA Champions League places.
Arkadiusz Milik volleyed against the post and then saw a header pushed onto the woodwork by Thomas Strakosha before Jose Callejon fired the hosts ahead with his first goal of the season in the 34th minute.
Milik doubled Napoli's tally three minutes later by curling an exquisite free-kick into the top corner.
Fabian Ruiz smacked a left-foot shot against the top of the upright early in the second half but Ciro Immobile reduced the arrears in the 65th minute with a shot through the legs of defender Raul Albiol.
Despite having Francesco Acerbi sent off for a second yellow card shortly afterwards, Lazio did enough to make Napoli's life uncomfortable towards the end and the final whistle was greeted with huge relief by the San Paolo crowd.
Napoli, with 47 points, opened up a seven-point gap between themselves and third-placed Inter Milan while Roma's 3-2 win over Torino the previous day took them fourth, the last of the Champions League places, with 33. Lazio are a further point behind in fifth.
