Second-half goals from Gohkan Inler, Goran Pandev and Blerim Dzemaili put Napoli on 69 points, eight behind leaders Juventus who visit local rivals Torino on Sunday.
The victory also sees Napoli move 10 points clear of third-placed AC Milan, who host Europa League-chasing Catania in Sunday's late game, and 11 in front of Fiorentina.
"It wasn't an easy game and you could see that in the first half," forward Pandev told Sky Sport Italia. "Often we've messed up matches like this in the past, but today it went well."
Roberto Pereyra's curling strike after 56 minutes was enough to put Francesco Guidolin's Udinese on 54 points, one ahead of Inter Milan who visit relegation-threatened Palermo on Sunday.
Bologna had Alberto Gilardino's goal to thank for a 1-1 draw at Atalanta in Saturday's early kick off after he cancelled out Luigi Giorgi's 67th minute opener with 14 minutes left.
Cagliari, who had striker Mauricio Pinilla sent off in added time, stay 10th on 42 points, two points and one place above Bologna.
Atalanta leapfrogged Sampdoria into 14th spot on 39 points, 10 clear of the relegation zone, while Pescara stay bottom on 23 points.
Napoli dominated the opening exchanges but without striker Edinson Cavani they were initially less than clinical in front of goal, with Miguel Britos and Lorenzo Insigne wasting good chacnes to head their side in front during the first half-hour.
Insigne thought he had given the visitors the lead with a powerful finish after Dzemaili's tackle saw the ball drop to him just inside the area but his effort was ruled out as the Napoli players celebrated.
Pescara, who had to win to have any realistic chance of Serie A survival, could have taken a shock lead in the 38th minute when Giuseppe Sculli was put through, only for the striker to scoop his shot over the bar.
However Inler put Napoli in front 41 seconds after the interval when the ball broke to him and his long-range shot took a huge deflection which helped the ball past already committed Pescara keeper Ivan Pelizzoli.
That slice of luck calmed Napoli's nerves and, although Sculli forced a decent save from Morgan De Sanctis with a header in the 57th minute, Pandev doubled their lead a minute later.
The Macedonian brilliantly controlled a drilled Christian Maggio cross before spinning and calmly stroking the ball home.
Insigne should have scored in the 80th when, after racing clean through on goal, he dragged a poor shot wide but Napoli had their third two minutes later when Dzemaili thumped an unstoppable drive from distance into the top corner.
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- Goran Pandev