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.
Pat on the back: A cracker from Xhaka
Xhaka's free-kick lit up a game that had for long periods been low on cutting edge. All four of his Premier League goals have come from outside the box and, though he is more widely known for his combative attributes, this was a performance in which his creative side shone through, as further evidenced by his role in the second goal.
Boot up the backside: Newcastle defence crumbles without captain
Newcastle had been comfortable in defence in the first half but the withdrawal of Lascelles resulted in a complete loss of organisation and composure from the Magpies defence. Clark and Fernandez had to switch positions in the centre upon his introduction but Rafael Benitez will see that as no excuse for the collapse of his back four.
Key Opta facts:
- Arsenal have won consecutive Premier League away games for the first time since May 2017.
- One point from five games represents Newcastle's joint-worst start to a Premier League campaign (also 1999-00).
- Arsenal have failed to keep a clean sheet in any of their first five games to a top-flight season since the 1988-89 campaign.
- All 10 of Arsenal's Premier League goals this season (including own goals) have been scored by different players.
- Arsenal's Mesut Ozil has had a hand in four goals in four Premier League appearances against Newcastle (3 goals, 1 assist).
Arsenal welcome Ukrainian side Vorskla Poltava to Emirates Stadium in their opening Europa League clash before hosting Everton. Newcastle get a break from pitting themselves against the league's elite as they visit Crystal Palace.