The former Real Madrid man aimed a perfect volley into the top corner midway through the first half.
Here's a look at the teamsheet, via the Daily Mirror's John Cross:
The Gunners immediately took the initiative, surging forward and dominating possession. Newcastle dug in and prevented major early chances, but they also failed to make it out of their half much.
Alexandre Lacazette put Rob Elliot to work with a shot, and Jamaal Lascelles threatened with a header from a Mikel Merino free-kick.
DeAndre Yedlin fired over, and Alexis Sanchez didn't fare any better on the other side of the pitch. Ainsley Maitland-Niles also created an opening with a great run, but the finish wasn't there, as he found the side netting.
Arsenal FC News noted the youngster, who played out of position at left-back, performed quite well early on:
The Magpies dealt well with the threats from the hosts until just past the midway point of the first half, when Ozil broke the deadlock with a wonder strike. Newcastle failed to clear their lines, and the German powered home a beautiful volley that left Elliot looking.
James Olley of the London Evening Standard thought Ozil's decision to go for accuracy, rather than power, was key:
Arsenal kept pushing, and Granit Xhaka had a chance to double the lead, but his hard shot flew wide of the mark. Lacazette had a penalty shout after he was dragged down, but no spot-kick was given, and Ozil had a shot blocked from a promising position.
The first half included a late stoppage, as Merino and Nacho Monreal required treatment after a clash of heads, and momentum disappeared.
Goal's Chris Wheatley liked what he saw from the Gunners in the first half:
The second half got off to a slow start, and the first real chance fell to Alex Iwobi, who almost got to the ball first after Elliot couldn't gather it. Lacazette fired a shot over the crossbar, and substitute Matt Ritchie followed suit.
Petr Cech intervened to deny Jacob Murphy, and Lacazette should have done better on the hour mark, lifting the ball over the goal after a great pass from Ozil.
Per Olley, when the Frenchman was taken off, some fans let him know they didn't approve of his poor showing:
Elliot did well to keep out a hard drive from Jack Wilshere, and Joselu almost found an equaliser after his shot took a wicked deflection. Newcastle pushed for a goal late, and Ayoze Perez found some space but aimed a shot over.
He went wide shortly after, and the Magpies continued their push. It didn't yield any results, however, and the Gunners clung on for the win.