Shkodran Mustafi headed an eighth-minute opener and Pierre Emerick-Aubameyang fired a belated second just before the hour-mark, before Henrikh Mkhitaryan added a third 13 minutes from time as Arsene Wenger's selection gamble with AC Milan in mind paid off.
The hosts had escaped punishment for a profligate first half and were indebted to Petr Cech for saving a Troy Deeney penalty just minutes after Aubameyang struck, the goalkeeper finally recording his 200th Premier League clean sheet.
Wenger's scrutinised side remain 10 points adrift of the top four, having played a game more, but victory at a stadium once again pockmarked by empty seats will at least help boost still-fragile confidence ahead of a Europa League last-16 showdown pivotal to their season.
Deeney had memorably accused Arsenal of lacking 'cojones' at Vicarage Road in October but after responding to their critics with a 2-0 win in Italy on Thursday, the Gunners set a brisk tempo despite six changes that saw Laurent Koscielny and Aaron Ramsey rested.
Ozil had slipped Aubameyang through with just two minutes on the clock, Hornets 'keeper Orestis Karnezis splayed to thwart him, but the German created the opener soon after with an inswinging free-kick that Mustafi rose between yellow shirts to meet.