The Spaniard netted the winner after Lorenzo Insigne had ended his goal drought in cancelling out Fabio Quagliarella's opener at the San Paolo
Fabio Quagliarella broke the deadlock after just 14 minutes of play but Lorenzo Insigne levelled matters just after the break.
Callejon then struck with 18 minutes to go to earn Napoli a third win on the bounce in all competitions, after last weekend's win at Serie A rivals Sassuolo and the midweek success at Slovan Bratislava in the Europa League.
Three points did not look likely for Napoli during the early stages, with Torino starting the far better of the two sides. Indeed, Kamil Glik had already headed a Marco Benassi cross wide when Quagliarella opened the scoring against his former club.
The striker appeared to be in an offside position when he beat Rafael from an acute angle with a well-struck volley but the linesman's flag stayed down.
Napoli responded well to their early setback, though, with Insigne striking the bar before then seeing Jean-Francois Gillet pull off a fine instinctive save after being put through on goal.
Michu struck the bar with a header just after the break but Napoli did not have to wait much longer for a deserved equaliser, with Insigne nodding home a cross from Juan Camilo Zuniga.
It was the Italy international's first goal of the season and the forward, who has endured a fractious relationship with the San Paolo faithful, appeared overwhelmed by emotion after breaking his duck.
Napoli poured forward in search of a winner and it arrived in the 72nd minute, albeit in fortuitous circumstances, with a wicked bounce enabling Callejon's cross-cum-shot to loop over Gillet.
Torino could have snatched a point in the dying seconds but Rafael pulled off a brilliant save to deny Alessandro Gazzi and propel Napoli into seventh place in the Serie A standings.