Both Inter coach Walter Mazzarri and Napoli boss Rafael Benitez were challenging their former clubs with a certain amount of pressure on their shoulders following sluggish starts to the season.
There was anxious stalemate in Milan until Jose Callejon scored the first of his two goals with just over 10 minutes remaining.
When substitute Fredy Guarin levelled it looked like Inter had done enough to rescue a point, but they were forced to mount one last rally after Callejon converted his brace in stoppage time.
Hernanes' header may have denied seventh-placed Napoli two points but did little to further Inter's own frustrated ambitions of reaching the European places. They climb one spot to ninth.
Keisuke Honda scored twice as a resurgent AC Milan broke into the Champions League places with a 3-1 win at Hellas Verona.
The Rossoneri, who were helped along the road to victory by Rafael Marques' early own goal, climbed to fourth place in the Serie A table thanks to Japan forward Honda's well-taken brace.
Ambitious Verona fought hard to rescue a share of the points and a late rally did see Nico Lopez grab a consolation goal, but Rafael Marquez's dismissal called time on their brave challenge.
Cagliari came from two goals behind to grab a 2-2 draw against Sampdoria, who ended the game with only 10 men.
Manolo Gabbiadini and Pedro Obiang had Sampdoria on course for their fifth win of the season, but a red card to Fabrizio Cacciatore and a penalty just shy of the hour mark proved to be the turning point in the game.
Danilo Avelar converted from the spot before Marco Sau earned Zdenek Zeman's men a point.
Lazio climbed further up the Serie A table with their third win in a row thanks to a 2-0 triumph at Fiorentina on Sunday.
Filip Djordjevic and Senad Lulic scored the goals for the Biancocelesti to lift them three points clear of their hosts and into the hunt for the European places.
Lazio had the better of the first half, taking the lead with Djordjevic's fifth goal of the season, but Fiorentina had chances to level in the second half before Lulic scored on the break to seal his side's win.
Udinese will be glad to see the back of Turin after losing in the Piedmont city for the second time this season with Torino notching a 1-0 victory.
Their former forward Fabio Quagliarella did the damage at the Stadio Olimpico to inflict only the second defeat on Andrea Stramaccioni's side this season, the other a 2-0 loss to city rivals Juventus.
Quagliarella scored his fourth goal in as many Serie A games on the hour mark, but chose not to celebrate out of respect for his former club.
Substitute Richmond Boakye condemned hapless Parma to a fourth straight Serie A defeat as Atalanta claimed their first home win of the season with a 1-0 win.
The Ghanaian striker appeared on the Stadio Atleti Azzurri d'Italia pitch for only 14 minutes but provided the key to unlock a Parma defence which looked ready to register a rare clean sheet.
Remarkably, Boakye's last-gasp goal was only a third of the entire campaign for profligate Atalanta, but their victory propels them into mid-table while Parma remain mired in the relegation zone.
Palermo picked up their first win back in Serie A to ease the pressure on their coach Giuseppe Iachini, although they left it late to beat 10-man Cesena 2-1.
Pauli Dybala put the Rosaneri in front after 33 minutes, but substitute Alejandro Rodriguez levelled from the penalty spot on the hour mark.
Manuel Coppola was given his marching orders for a second yellow card with 10 minutes to go and Cesena were unable to hold on to a point as Costa Rica defender Giancarlo Gonzalez headed in Palermo's winner in the second minute of stoppage time.
