Özil's classy opener was followed by Olivier Giroud's close-range finish in the first 15 minutes, as Napoli struggled to contain their hosts' swift possession play.
Elsewhere in Group F, last year's runners-up Borussia Dortmund won their first game after defeat to Napoli two weeks ago. Robert Lewandowski scored twice and Marco Reus struck in their 3-0 conquest of whipping boys Marseille.
Cesc Fàbregas settled Celtic and Barcelona's contest with a late header after Bhoys captain Scott Brown was sent off. In the other Group H match, Ajax and AC Milan both scored in stoppage-time for a 1-1 draw.
Chelsea ran out 4-0 winners in Bucharest, as Ramires scored twice, Frank Lampard got on the scoresheet and Daniel Georgievski put through his own net in the rout. Schalke won at Basel, which leaves them top in Group E.
And in Group G, Atlético Madrid came from behind to win 2-1 at Porto after Zenit St Petersburg and Austria Vienna's bore draw.