Gonzalo Higuain also notched his 26th league goal of the season as Napoli, chasing their first title since 1990, ended a three-match sequence without a Serie A win.
Chiriches, replacing the suspended Raul Albiol in the centre of the defence, had a nightmare start when he was dispossessed by Nicola Rigoni who ran on and fired a 25-metre shot beyond keeper Pepe Reina in the second minute.
Napoli needed only four minutes to level when Faouzi Ghoulam pulled the ball back from the left and Higuain sidefooted home from 10 metres.
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The hosts went ahead seven minutes before halftime when Chiriches met Jorginho's corner with a flying header as the Romanian made up for his earlier mistake.
Napoli continued to create plenty of chances and Higuain went close to his second when a shot was tipped on to the bar by Albano Bizarri in the 65th minute.
Jose Callejon made the game safe for Napoli when he turned in a cross after 70 minutes.
Napoli and Juventus, who visit Atalanta on Sunday, have 61 points and the same head-to-head record, meaning Napoli are top on goal difference.
Sampdoria eased their relegation worries by scoring three times in the opening half-hour in a 3-0 win at bottom club Verona.
Roberto Soriano, Antonio Cassano and Lazaros Hristodoulopoulos were on target for Samp who put eight points between themselves and the relegation zone.
Verona have 18 points and are nine adrift of safety.
(Writing by Brian Homewood; Editing by Tony Jimenez)
