With the score delicately poised at 2-1, a debatable sending-off for Antonio Bocchetti turned the game and the hosts didn't look back.
Cavani returned to the starting lineup after suspension, while Lorenzo Insigne started against the club he fired to Serie B glory last season. Giandomenico Mesto deputised for the injured Christian Maggio.
Ante Vukusic and Vladimir Weiss earned starting places for the visitors, who were without the injured Giuseppe Colucci, Manuele Blasi, Juan Fernando Quintero and Jonathas. Defender Antonio Balzano was suspended.
The hosts put Pescara under the cosh straight from the kick-off. After Insigne fired wide and Mattia Perin turned Hamsik's solo effort around the post, Napoli took the lead on nine minutes.
Inler controlled the ball outside the box, brought the ball onto his right foot and fired a screamer that swerved through the air and nestled into the roof of the net.
Six minutes later, the home side doubled their advantage. Half-hearted defending allowed Insigne's deflected ball to find Hamsik in the box. The Slovakian brought it down and bamboozled two defenders with quick feet and a scuffed shot somehow crept into the far corner.
The visitors cut the deficit on 18 minutes. Damiano Zanon's cross was headed in by Birkir Bjarnason, who rose above Mesto to loop the ball into the far corner.
Just before the half hour mark, Valon Behrami's hopeful 30 yard drive was deflected wide.
Pescara came back into the game. Paolo Cannavaro had to stick out a leg to block Bjarnason's shot, while Vukusic scooped over a close range effort when he should really have done better. Pablo Zuniga foolishly wrapped his arms around Vukusic in the box. Bizarrely, no-one batted an eyelid and Napoli went on the counter-attack. Cavani was given space to chest down and blaze wide. The Uruguayan then sprung the offside trap, but Perin ran out to force the Hitman into a quick decision and snuff out the chance.
Six minutes before the break, Perin spilt Inler's shot and Christian Terlizzi had to intercept to stop Cavani from pouncing on the rebound.
In the second half, Napoli pressed for a third. Cavani brought down a long Cannavaro ball, didn't manage to get enough power in his shot, but Perin still pulled off a fine point blank stop.
Controversy struck on 57 minutes. Cavani skipped past Terlizzi's challenge in the box, but went down under Bocchetti. The defender seemed to get some of the ball, but was harshly given a straight red card. Cavani buried the resulting spot kick hard and low, underneath Perin's body.
The home side were now in complete control. Five minutes after his first goal, Cavani smashed home a second into the roof of the net, after Hamsik rolled the ball across the box. It was Cavani's 10th goal in 12 league games so far this season.
Pescara were denied a clear penalty with 20 minutes to play after Bjarnason went down under Cannavaro.
Insigne was quickly sent clear, but was denied the chance to score a certain fifth when play was pulled back for a Zanon foul. The referee realised his mistake at not letting the play continue, but still booked Zanon.
Cavani was chasing a hat-trick and the match ball, but saw an acrobatic volley saved. Inler did claim his second on 78 minutes. Once again, the Swiss midfielder picked up the ball outside the box, putting his laces through it to smash a fifth goal in off the post.
With a minute to play, substitute Eduardo Vargas squandered a chance when it was easier to square the ball to Cavani.
In stoppage time, Cavani exposed Pescara's high defensive line yet again, but bent his shot the wrong side of the post.
Napoli: De Sanctis; Gamberini, (Dzemaili 70) Cannavaro, (El Kaddouri 81) Britos; Mesto, Behrami, Inler, Hamsik, Zuniga; Insigne, (Vargas 76) Cavani
Pescara: Perin; Romagnoli, Terlizzi, Bocchetti; Zanon, Bjarnason, Togni, (Nielsen 75) Cascione, Modesto; Weiss; (Capuano 65) Vukusic (Abbruscato 67)
Goals: Inler 9, 78 (N) Hamsik 15 (N) Bjarnason 18 (P) Cavani pen 58, 63 (N)
Sent-off: Bocchetti 57 (P)