Sofyan Amrabat scored a consolation just seconds from the end. Insigne scored after just seven minutes, stealing possession near the centre circle and rapidly sprinting straight upfield before firing home past the outstretched arm of diving goalkeeper Brad Jones.
Napoli captain Marek Hamsik went narrowly wide as the hosts looked to increase their lead before halftime but it took just four minutes after the break for Mertens to tuck away a gift back pass from Feyenoord defender Kevin Diks for a 2-0 lead.
But the Dutch champions might have made a contest of it after being awarded a penalty when Steven Berghuis was brought down in a double challenge from Napoli’s two African internationals Faouzi Ghoulam and Kalidou Koulibaly in the 67th minute.
But 35-year-old Reina made a good save to deny Feyenoord, who had also squandered a penalty at the weekend in the Dutch league.
Two minutes later the contest was effectively over after another defensive error, this time from Renato Tapia, allowed Callejon to score from a tight angle.
Reina made a point blank save to deny a shot from Berghuis that deflected off his own team mate Tonny Vilhena as Feyenoord’s fortunes continued to flounder.
But Amrabat burst through the defence to score three minutes into stoppage time. It was Feyenoord's first goal in this season's competition.
Feyenoord had marked their return to Champions League after a 15-year absence with a 4-0 home loss to Manchester City in their opening group game.
(Reporting by Mark Gleeson, editing by Pritha Sarkar)
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