Calls for Napoli's new coach, Maurizio Sarri, to be sacked have grown increasingly louder in recent weeks after his team failed to win any of their opening three league games.
Last week the club's former striker, Diego Maradona, hit out at Sarri claiming the former Empoli handler was “not the right man for the job”.
Sarri responded to the criticism by steering his side to a 5-0 defeat of Club Brugge in the group stages of the Europa League on Thursday.
And the hosts showed that win was no flash in the pan with a determined, focused performance against a Lazio side that lacked ambition and intensity and quickly ran out of ideas before being overrun in a one-sided second half.
Sarri has so far refused to be goaded by Maradona's comments and on Sunday told Sky Sport: “Maradona can think what he likes. He is still my idol.”
He added: “We played well, we had the right approach and we got right on top of our opponents from the start.”
Lazio ended last season as one of the form teams in Italy's top flight and they started this season in positive fashion with two wins and a draw.
But they were found lacking in all departments, only really showing any enterprise after Felipe Anderson came off the bench to replace captain Stefano Mauri at the start of the second half.
Lazio coach Stefano Pioli told Sky Sport: “I don't think we showed our true face tonight. We had problems dealing with Napoli's pace and intensity from the outset.
“We made too many mistakes and we weren't compact enough. It's a heavy defeat and we have to show from our next game that we can play a lot better.”
Napoli went in for the half-time interval with a 2-0 lead after goals by Higuain, who turned his marker before beating Marchetti with a superb strike, and Allan although it could have been more.
Lorenzo Insigne was a constant thorn in Lazio's side and after coming close on several occasions, the diminutive winger finally hit the target three minutes after the restart when he tapped home the rebound from a Higuain strike.
Higuain grabbed his second just before the hour mark after powering on to Elseid Hysaj's through-ball, riding a challenge by Wesley Hoedt and beating Federico Marchetti at the 'keeper's far post to claim his fourth league goal in four games.
The Argentinian international left to a standing ovation in the 64th minute when he was replaced by Manolo Gabbiadini, who took little time in adding his name to the scoresheet.
With 11 minutes remaining the Italy international coolly ran on to Allan's through-ball to slip the ball past the hapless Marchetti.
The last time Lazio's suffered a 5-0 league defeat was against Udinese in September 1984.
Napoli's first win of the campaign moved them up to 11th place, seven points behind leaders Inter Milan, with Lazio one point and one place in front.