Granit Xhaka and Mesut Ozil - on his 200th Arsenal appearance - netted early in the second half and although Newcastle halved the deficit through Ciaran Clark in added-on time, Arsenal were full value for the three points.
The Gunners now find themselves in seventh place in the league standings, while Newcastle are 18th and remain without success from their opening five matches in the top flight this season.
Newcastle went into the game having failed to show much attacking intent in their last home fixture against Chelsea, but it was a different story against the North Londoners who found themselves under pressure during the opening quarter-of-an-hour.
Arsenal were putting themselves in trouble with Newcastle taking advantage of the slow build-up play of the visitors, but it would not lead to any shots on goal from the home team.
Petr Cech had to remain alert throughout the first 45 minutes, but the Czech stopper was relatively untroubled aside from having to punch clear a headed cross from Jacob Murphy with two Newcastle players lurking at the back post.
Arsenal grew into the game as the half progressed with Alexandre Lacazette firing into the side-netting, while Aaron Ramsey should have teed up Pierre-Emerick Aubameyang for a tap-in rather than sending a cross high over the crossbar.
However, Arsenal's opener came from a player whose place in the side is frequently disputed, with Xhaka firing a stunning free kick into the top corner of Martin Dubravka's net from 30 yards.
Newcastle needed a response but Arsenal doubled their advantage nine minutes later when Ozil forced a shot under Dubravka from 16 yards out after Lacazette's initial goalbound effort had been brilliantly blocked.
Arsenal quickly suggested that they were not prepared to see out the remainder of the game by surging forward in search of a third, but Aubameyang could only fire wide of the far post after being picked out by Lacazette at the back post.
Newcastle were still unable to create anything of note at the other end of the pitch, and Arsenal only grew in confidence with a last-ditch block being required to prevent Henrikh Mkhitaryan from finding the far bottom corner.
Arsenal had more opportunities to further extend their lead, but the best chance of the remaining minutes of normal time went to Newcastle with Joselu seeing a header tipped over the crossbar by Cech.
The visitors looked comfortable heading into three minutes of added-on time, but Clark gave Newcastle a lifeline by powering in a header from eight yards after being left all on his own at the back post.
However, Arsenal were able to cope with the late blip to get their third successive win on the board, moving level on points with North London rivals Tottenham Hotspur.
NEWCASTLE UNITED (4-4-1-1): Dubravka; Yedlin, Lascelles (Clark 46'), Fernandez, Dummett, Ritchie (Muto 79'), Hayden, Diame, Murphy (Kenedy 69'); Perez, Joselu
ARSENAL XI (4-3-3): Cech; Bellerin, Mustafi, Sokratis, Monreal; Xhaka, Guendouzi (Torreira 46'), Ramsey (Welbeck 80'); Ozil, Aubameyang (Mkhitaryan 69'), Lacazette