Napoli are within two points of leaders Juventus thanks to Marek Hamsik's second-half goal which moved them above an Inter side undone by Nicola Sansone's fine individual late strike.
Juventus, who lost 1-0 at AC Milan on Sunday, have 32 points from 14 games with their lead cut from four points with Napoli now on 30 above Fiorentina and Inter who are level on 28.
Napoli, without suspended striker Edinson Cavani and the injured Goran Pandev, made hard work of beating Cagliari, with Hamsik's 73rd minute goal enough to earn the three points.
The visitors looked flat at times although young striker Lorenzo Insigne went close to scoring either side of the half-hour mark, hitting the post and later dragging a shot wide.
Cagliari appealed for a penalty when Alessandro Gamberini upended midfielder Daniele Conti, who then directed a Thiago Ribeiro corner against the post just before the break.
Napoli were on the back foot for much of the second half but scored when Juan Zuniga ran into the box in the 72nd and found Hamsik who struck the ball past keeper Michael Agazzi, sparking Cagliari protests that the Slovakian was offside.
"It was a difficult game, but we did really well," Napoli coach Walter Mazzarri told Sky Italia. "We suffered a bit during the second half, but I have to compliment my team.
Turning to his side's chances of winning Serie A, he added: "I'm really not thinking about the title. We'll see where we are at the end of the season."
MINI-SLUMP
Inter's recent mini-slump had seen them lose at Atalanta and draw against Cagliari and their fortunes were not about to improve at Parma, who have moved up to seventh on 20 points.
To add to their woes the Nerazzurri were without suspended creative outlet Antonio Cassano while the saga surrounding Wesley Sneijder's future has been an unwelcome distraction, the Dutchman having been asked to accept a reduced wage package.
Coach Antonio Stramaccioni had called for "hunger and grit" on the eve of the game but instead Inter looked timid and tired, struggled to link up midfield with attack and frequently found themselves chasing the ball against a hard-working Parma team.
The hosts had most of the possession in the first half but failed to make it count with Inter goalkeeper Samir Handanovic comfortably dealing with a tame Amauri shot and also keeping out attempts from the lively Jonathan Biabiany and Gabriel Paletta.
With Parma snapping at their heels and closing down the midfield, Inter struggled to find space despite the best efforts of seasoned campaigner Esteban Cambiasso, whose 36th-minute header was cleared off the line by Jaime Valdes.
The visitors had a bit more bite after the break but Parma held their nerve and continued to cut off the supply lines to Inter's ineffective front pair Diego Milito and Rodrigo Palacio.
Parma took a 75th-minute lead when Sansone ran 40 metres, easing his away from two defenders before calmly slotting the ball past Handanovic with a neat right-foot shot.
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