After opening defeats to Manchester City and Chelsea, Arsenal have found their groove under Unai Emery against lesser opposition and they survived a poor first half to see off winless Newcastle.
Xhaka opened the scoring in stunning fashion, beating Martin Dubravka from 25 yards, and he played a part in the second as Ozil effectively sealed the points.
Newcastle's heads dropped thereafter and, despite Ciaran Clark's stoppage-time header, they have just the solitary point from a daunting start to the season, while Arsenal's bid for a return to the top four is gathering steam.
Goalkeeper Petr Cech and the Arsenal backline looked shaky with the ball at their feet and continually invited pressure in the early stages, and the shot-stopper was required to beat away a Jacob Murphy diving header at the far post.
Lucas Torreira was brought on for Matteo Guendouzi for the start of the second half while Newcastle were forced into a change at the back with injured captain Jamaal Lascelles replaced by Clark.
Three minutes into the second half that reworked back four was breached as Federico Fernandez fouled Pierre-Emerick Aubameyang and Xhaka unleashed a wonderful curling free-kick that left Dubravka helpless.
And Arsenal moved into complete command nine minutes later when Ozil's low finish beat the hand of Dubravka after Alexandre Lacazette's initial effort from Xhaka's left-wing pull back was blocked.
Aubameyang then fired narrowly wide at the far post but his wastefulness ultimately went unpunished as Arsenal saw the game out following Clark's header from Fernandez's cross.
What it means: Arsenal produce further show of resilience
Having found life difficult for much of the first half, Saturday's contest had the look of one in which Arsenal would normally crumble. But the Gunners were resilient in beating Cardiff City 3-2 last time out and a similar steel was on show at St James' Park as they shook off their earlier jitters to ultimately emerge comfortable winners.
