The 30-year-old striker opened the scoring and then, after the visitors had replied through Gonzalo Higuain and Jose Callejon, struck again right at the death
The 30-year-old striker gave the hosts the lead seven minutes before the break but the Partenopei levelled courtesy of a Gonzalo Higuain penalty before then edging ahead through Jose Callejon.
Panagiotis Kone's dismissal appeared to end Bologna's hopes of getting anything out of the game but, remarkably, Bianchi equalised in injury time to leave Rafael Benitez and his troops shell-shocked.
With both Serie leaders Juventus and second-placed Roma having won on Saturday, Napoli had arrived in Emilia-Romagna knowing that nothing less than three points would suffice if they were to keep their faint title hopes alive.
However, they struggled with a saturated pitch and Bianchi had already gone close with a header when he deservedly put the home side ahead seven minutes before half-time.
The former Manchester City man momentarily lost Raul Albiol and glanced home Alessandro Diamanti's terrific ball from the left-hand side.
The goal very nearly prompted an instant riposte from Napoli but Callejon headed over moments later.
Higuain was then guilty of an atrocious miss on the hour mark, when he somehow contrived to nod wide from no more than five yards out.
However, the Argentine made amends a couple of minutes later when he fired home emphatically from 12 yards out, after Kone had clumsily bundled over Blerim Dzemaili in the area.
Napoli then edged in front when a blistering counterattack ended with Callejon finding the bottom right corner of the Bologna net with a sweet right-footed strike.
Kone was then dismissed for a second booking with just six minutes to go, but the Rossoblu refused to give in and got their reward in the dying seconds when Bianchi calmly blasted the ball home after it hard dropped for him at the back post.
It was a crucial strike, as it moved Bologna out of the relegation zone, while at the same time cutting Napoli's lead over fourth-placed Fiorentina to just three points.