Napoli, who had won their opening eight league games, could find no way past the Slovenian as both teams remained unbeaten, with the hosts on 25 points and Inter on 23.
It was the first time since a 2-0 home defeat by Atalanta in February that Napoli had failed to score in a league match and their first failure to win one since a 2-2 draw at Sassuolo in April - a club record 13 games.
Maurizio Sarri's side played their usual flowing football in midfield but Inter's defence held firm as coach Luciano Spalletti's cautious approach paid off.
Handanovic made a superb double save to parry a Jose Callejon shot and then block Dries Mertens' effort from the rebound and also frustrated Lorenzo Insigne when he was given a free header by Marek Hamsik's diagonal pass.
Napoli goalkeeper Pepe Reina made two saves just before halftime when he blocked Mauro Icardi's shot at the near post and punched Borja Valero's volley over the crossbar.
Matias Vecino nearly gave Inter the lead early in the second half after running half the length of the pitch and exchanging passes with Icardi but his chip from a narrow angle was cleared off the line by Raul Albiol.
The final 20 minutes were nearly all Napoli as Insigne sent a shot flashing past the post, then Handanovic stopped Piotr Zielinski's drive and prevented team mate Miranda from scoring an own goal with a reflex save from point-blank range.
Earlier, Sampdoria maintained their perfect home record when they thumped hapless Crotone 5-0, with five players sharing the goals.
Defender Gian Marco Ferrari began the rout by heading in from a free kick in the third minute against his former club and Fabio Quagliarella drilled home a penalty eight minutes later after Duvan Zapata was hauled back in the area.
Colombian Zapata also set up the third in the 38th minute when he held off a challenge to reach the byline and provide an easy chance for Gianluca Caprari to turn the ball in at the far post.
Karol Linetty put the finishing touch to a well-worked move in the 71st minute and substitute Dawid Kownacki pounced on a poor clearance by Crotone goalkeeper Alex Cordaz five minutes later to complete the scoring.
Sampdoria, who have won four out of four at home, moved up to fifth with 17 points from eight games while Crotone, who pulled off a great escape to avoid the drop last season, are 16th with six.
(Writing by Brian Homewood in Berne; Editing by Christian Radnedge and Pritha Sarkar)
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