The ambitious southerners have a particularly poor recent record against Chievo, who find themselves struggling to avoid relegation once again, and the bizarre trend looked set to continue when Gennaro Sardo scored early on.
An abysmal miss from Gonzalo Higuain set the tone for Napoli's frustrating evening, with Dries Mertens particularly profligate at the Stadio San Paolo, yet Spanish defender Albiol finally nicked a late goal to stop Chievo claiming a fifth win from eight recent encounters between the clubs.
Napoli could have closed to within a point of second-placed Roma but sit only four points clear of Fiorentina while Chievo are 16th, one point clear of the drop zone and winless in six games.
Mertens was first to threaten, the Belgian nodding the ball just over Rafael Cabral's goal from a Christian Maggio cross, but it was Chievo who opened the scoring in the 18th minute.
Hush descended among the home fans at the San Paolo as Sardo latched onto Cyril Thereau's pass to rifle a scorching shot under the crossbar from distance, and from an awkward angle.
It took Napoli's players a while to compose themselves and there were clearly some nerves jangling among the forwards when Jose Callejon screwed wide from a good position when put through by Marek Hamsik.
Moments later, the Spaniard tried to make amends by picking out Higuain, who was sprinting unchecked to the far post.
Inexplicably, the former Real Madrid hitman slammed the ball across the goalmouth and back into play.
Mertens was the next man to fluff his lines as he rattled a post with a left-footed screamer and, five minutes before the break, the winger wasted Gokhan Inler's through ball by guiding it well wide of the mark.
Callejon did much better as the interval approached, only for Christian Puggioni to palm his low drive around a post, and Chievo finally threatened once more with Rafael repelling Boukary Drame's left-footed sighter.
When play resumed there was much more frustration to come for Rafael Benitez's men, who continued to dominate while failing to put any of their chances away.
Albiol, Higuain and Inler all missed the target before the hour mark and, as the pressure on retreating Chievo reached breaking point, Mertens again clattered a post, this time with a rising drive from an improbable position.
Attacking midfielder Jorginho, signed this week from Hellas Verona, made his Napoli debut from the bench and was soon on the attack, driving Hamsik's assist just past a post.
There were three minutes remaining when yet another Mertens effort ended up with the fans, and it seemed Napoli were fated to suffer another defeat to their bogey team.
It took an unspectacular goal from Albiol to partly spare their blushes, and rescue a point, as the centre-back's close-range finish found its way into the bottom corner two minutes before the final whistle.