Rudi Garcia's men have seen their title hopes all but disappear in the wake of defending champions Juventus' incredible form, and now their grip on second spot is loosening.
Callejon leapt highest to connect with Faouzi Ghoulam's superb cross from the left wing as he headed home from close range to seal the points just nine minutes from time.
The Spaniard's 10th Serie A goal of the season, and first this year, boosted Napoli's hopes of securing an automatic UEFA Champions League qualification spot.
Roma suffered a big blow in the first half as midfielder Kevin Strootman limped off with an injury and things looked to have got worse for them when Alessandro Florenzi's free-kick was headed in by Mehdi Benatia, but he was flagged offside.
The game was full of missed chances and it came down to Callejon to settle matters late on, inflicting Roma's second league defeat of the season.
Juventus equalled the Serie A record of 14 consecutive home wins with a 1-0 victory over Fiorentina at Juventus Stadium. Antonio Conte's side are now level with Torino's record from the 1975-76 campaign and have opened a 14-point lead over Roma.
Kwadwo Asamoah scored the only goal as Juventus drew first blood in their triple-header with Vincenzo Montella's side.
The sides are set to meet three times in less than a fortnight, with Sunday's Serie A clash to be followed by two encounters in the UEFA Europa League last 16.
Lazio suffered a 1-0 loss to Atalanta at a sparsely populated Stadio Olimpico as their fans staged a stay-away protest against club president Claudio Lotito. Despite the result Lazio remain in eighth after Torino were beaten 1-0 by Inter, with Rodrigo Palacio heading the winner.
Sampdoria scored four second-half goals to recover from 2-0 down to seal a 4-2 home victory over Livorno. The away side remain in the final relegation place and two points adrift of safety.
Alberto Paloschi helped Chievo seal a 2-1 victory over Genoa after converting two penalties for Eugenio Corini's side, eclipsing Alberto Gilardino's late leveller.
Elsewhere, Parma climbed to sixth with a 2-0 win over Verona, while rock-bottom Sassuolo ended their seven-game losing streak with a 0-0 draw at Bologna.
