Higuain ended a 71-day personal goal-drought when he put the visitors ahead in the 24th minute before an own goal from Valon Behrami brought Lazio level seconds later.
Goran Pandev put Napoli back in front early in the second half and Higuain made it 3-1 after 72 minutes.
Lazio substitute Keita Balde Diao gave the hosts a lifeline with three minutes remaining but Jose Maria Callejon would kill the game off in stoppage time.
The victory sees Napoli bounce back from successive defeats to Juventus, Parma and Borussia Dortmund in the last fortnight.
Napoli, who are third, have now closed the gap on second-placed Roma to three points while they have increased their advantage over nearest rivals Inter Milan to four points.
Lazio, meanwhile, have dropped to ninth position with their winless run extending to six league games.
Callejon was first to test Federico Marchetti with a stinging drive that the Laziogoalkeeper was forced to palm over the bar.
The visitors silenced the home crowd by taking the lead midway through the first half.
Gokhan Inler fed Higuain in the box and the Argentinian forward struck the ball beyond Marchetti and into the back of the net.
Napoli's joy was shortlived, however, as Lazio equalised one minute later.
Behrami's poor attempt to clear Antonio Candreva's cross stunned Napoli goalkeeper Pepe Reina and hit the back of his net.
Lazio should have taken the lead before half-time but Candreva's angled shot from inside the box went wide.
Napoli pressed forward after the break and were rewarded in the 50th minute when Christian Maggio found Pandev in the box, the former Lazio player striking the ball past Marchetti from six yards.
Pandev then turned provider when he spotted an unmarked Higuain in the area and the South American's close-range effort went in.
But with three minutes remaining, Keita got past two defenders and drilled home a right-footed shot from 12 yards.
Napoli would had the last say, though, as Callejon beat Marchetti with a shot from 12 yards to secure all three points for the visitors.