Mertens, who had not scored in 910 minutes previous to this encounter, netted his first to equalise following Bologna's shock opener after just 29 seconds.
The Belgian then curled an effort past Antonio Mirante in the second half to seal a sixth consecutive league win for the hosts, and send them above Juventus to the summit of the Italian top flight.
An action-packed first 10 minutes, which featured two goals and an injury, saw the game explode into life in its early stages.
Bologna striker Rodrigo Palacio, who had not found the net since September, rose above Mario Rui in the Napoli box inside the first 30 seconds and headed past Pepe Reina from Federico Di Francesco's cross.
The visitors suffered a setback moments later, however, when Simone Verde - who recently rejected a move to Napoli in favour of his current employers - pulled his hamstring and was duly replaced by Ladislav Krejci.
Palacio was then involved in Napoli's equaliser after putting his side in front. Mario Rui's cross deflected off the forward, which sent the ball looping over Mirante. Ibrahima Mbaye, who was credited with an own goal, could do nothing to stop the ball crossing the line.
Both sides settled into the tie after the frantic opening, with Palacio continuing to cause Napoli problems in attack. The Argentine was played through and beat Vlad Chiriches for pace, but his weak effort was parried by Reina.
Napoli then took the lead through a Mertens penalty. Jose Callejon squirmed his way behind Bologna defender Adam Masina, before the latter player was adjudged by a VAR referral to have pushed Callejon - Mertens made no mistake with the spot kick.
The two clubs sparred early on in the second half, without producing any real chances.
Mertens made it 3-1, however, when a counter-attack led by Allan was finished off by the Belgian, who cut inside and whipped a shot into the far corner that left Mirante stranded.
The game petered out following Napoli's third, but the hosts made sure of the win with solid defence to move one point above Juve into top spot.
NAPOLI (4-3-3): Reina, Chiriches, Koulibaly, Hysaj, Rui; Jorginho (Diawara, 74), Allan, Hamsik (Zielinski, 66); Callejon, Insigne (Rog, 80), Mertens
BOLOGNA(4-2-3-1): Mirante; De Maio, Helander, Mbaye, Masina; Poli (Zapata, 82), Pulgar; Verdi (Krejci, 5), Dzemaili, Palacio (Destro, 73); Di Francesco