Miralem Pjanic's 15th-minute goal was enough to earn Rudi Garcia's men all three points, although they had to survive a storm at the Stadio Olimpico as Napoli pushed in vain for an equaliser.
The win ensures the giallorossi will remain second this weekend having put enough of a gap between itself and city rival Lazio.
The host had its best spell of the game in the opening 15 minutes, but then lost its way as Napoli asserted itself.
Fortunately for Roma, by that time it had taken the lead with Iturbe sending Alessandro Florenzi deep, and his pass back was swept into the bottom right-hand corner by Pjanic.
Inspired by an enterprising Dries Mertens, Napoli responded well, forcing its former goalkeeper Morgan De Sanctis to make a string of saves to keep Roma in front.
Jose Callejon wasted the best opportunity of the first half when faced with only De Sanctis to beat, but he showed a reluctance to shoot and, after defenders had got back, he instead set up Jonathan De Guzman, whose shot was blocked by Kostas Manolas.
Napoli continued to attack in the second half with De Sanctis again making an excellent instinctive save to turn substitute Manolo Gabbiadini's effort wide.
The Roma custodian made another save to deny Gabbaidini's shot from the edge of the area before Roma wasted the chance to wrap up victory on the break when Iturbe took the ball round Mariano Andujar, but shot into the side-netting.
Andujar went forward for a late corner as the azzurri searched for an equaliser, but it was not its day as Roma resisted despite some late drama inside its penalty area, winning at home for the first time since 30 November.
Juventus is on track for a fourth straight Serie A title with a 2-0 win over Empoli.
Carlos Tevez opened the scoring shortly before the interval and Roberto Pereyra added a second in stoppage time as the Bianconeri responded to wins from Roma and Lazio to restore a seemingly unassailable 14-point lead at the top with nine rounds to go.
Juventus also had goalkeeper Gianluigi Buffon to thank for making several fine interventions in the second half when Juve dropped its intensity, saving itself for a trip to Fiorentina in the Coppa Italia in midweek and the Champions League quarter-final clash with Monaco a week later.
Lazio kept the heat Roma, though, by clinching a seventh consecutive league win, 3-1 at 10-man Cagliari.
Miroslav Klose put the Roman outfit ahead in the 31st minute only for Marco Sau to pull Cagliari level four minutes into the second half.
Lucas Biglia put the visitor back in front on the hour from the penalty spot after Lorenzo Crisetig brought substitute Keita down in the area.
Inter Milan left the San Siro to a deafening chorus of boos from the home fans after a 1-1 draw with rock-bottom Parma.
Fredy Guarin gave Inter the lead in the 25th minute, but Andi Lila levelled just before half-time.
AC Milan picked up a first win away from home since mid-October, beating Palermo 2-1 at the Stadio Renzo Barbera.
Alessio Cerci gave Filippo Inzaghi's men the lead after 37 minutes, but a Paulo Dybala penalty brought the hosts level in the 72nd minute.
Jeremy Menez restored Milan's lead 10 minutes later, earning them all three points and keeping Milan's hopes alive of qualifying for Europe next season.
Alessandro Diamanti and Mohamed Salah's quick-fire goals gave Fiorentina a 2-0 win over Sampdoria.
Fabio Quagliarella and Kamil Glik gave Torino a 2-1 win over Atalanta, with Mauricio Pinilla pulling one back for the struggler.
Torino and Atalanta both ended the game with 10 men after Pinilla and Migjen Basha were shown red cards for fighting.
Substitute Davide Succi equalised nine minutes from time as Cesena hit back from 3-0 down to draw 3-3 at Hellas Verona.
The host appeared to be cruising to victory after two goals from Luca Toni and a third from Juanito Gomez but relegation-threatened Cesena hit back with three strikes in the last 20 minutes.
Substitute Carlos Carbonero scored the visitors' first and Franco Brienza's fantastic free-kick made it 3-2 with 13 minutes left.
Succi then pulled his team level as Cesena stunned the crowd in the Marc' Antonio Bentegodi stadium.
Cyril Thereau earned a 1-1 draw for Udinese after Sebastian De Maio put host Genoa in front, while Sassulo held on for a 1-0 win over Chievo after Domenico Berardi scored from the spot in the first half.
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