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Dries Mertens scored from the penalty spot with eight minutes remaining after Andy Robertson tripped Jose Callejon inside the box.
Napoli substitute Fernando Llorente added a second in stoppage time to put the result beyond doubt.
In the other Group E game, Salzburg made an impressive start with a 6-2 victory at home to Genk.
Chelsea misses penalty in loss
Valencia gatecrashed Frank Lampard's managerial bow in the Champions League by earning a morale-boosting 1-0 win at Chelsea.
Ross Barkley spurned a chance to equalise by missing the target from the penalty spot.
Spain forward Rodrigo Moreno gave the visitors the lead against the run of play in the 74th minute of the Group H game, getting the slightest of touches on a free kick from Dani Parejo to send the ball into the roof of the net.
Chelsea continued to threaten and were awarded a penalty after a VAR review spotted a handball by Valencia defender Daniel Wass, but Barkley sent the resulting spot kick on to the cross bar and over.
Valencia travelled to London reeling from a stinging 5-2 league loss at Barcelona in coach Albert Celades's first game in charge after the much-loved Marcelino was sacked to the bewilderment of players, who began a media blackout after the decision.
But they leave the English capital emboldened and with three points after producing a solid, professional display.
Dortmund holds Barca
Borussia Dortmund hit the woodwork and had a penalty saved before drawing 0-0 with Barcelona as Lionel Messi made his first appearance of the season for the Spaniards.
Barca's in-form 16-year-old Ansu Fati became the club's youngest player to feature in a UEFA competition when he started but failed to make any real impact before being replaced by fit-again Messi just before the hour mark.
Even after the Argentine took the field it was the Germans who were more dangerous, with captain Marco Reus' 57th minute penalty saved by Marc Andre ter Stegen and Julian Brandt rattling the crossbar with a thundering shot in the 77th.
In the group's other game Inter Milan were held to a 1-1 home draw by Slavia Prague.