Newcastle, who had manager Alan Pardew back on the touchline after his seven-game ban for headbutting Hull City’s David Meyler, were outplayed by a patient Arsenal side for whom Santi Cazorla, Aaron Ramsey and Mesut Ozil shone.
The opening goal came after 26 minutes when Laurent Koscielny barged Moussa Sissoko out of the way to prod home Cazorla’s chipped free-kick past Tim Krul.
Arsenal doubled their lead through Ozil’s tap-in at the far post on 42 minutes after Krul had twice denied Olivier Giroud with blocks from point-blank range.
Giroud then completed the scoring midway through the second half with a bullet header at the near post from Ozil’s driven cross.
The Gunners next face West Brom at the Emirates on Sunday knowing a win, or a defeat for fifth-placed Everton at home to Manchester City on Saturday, will ensure their qualification for the Champions League for a 17th successive time.
For Newcastle, it is a sixth consecutive defeat, their worst run for 27 years, and the supporters held up banners at the end calling for their manager Pardew to be sacked.
16’ - CHANCE! Ozil volleys wide from a Krul punch but the referee had already ruled that Koscielny had fouled the Dutchman.
25’ - GOAL! (Arsenal 1-0 Newcastle): Arsenal lead 1-0. Cazorla's free-kick bounces in the box and Sissoko fails to deal with the run of Koscielny, who pokes home from close range.
28’ - SAVE! Debuchy concedes a corner, Arsenal's fifth of the game so far. Podolski's header from Cazorla's corner is brilliantly saved one-handed by Krul.
41’ - GOAL! (Arsenal 2-0 Newcastle): Mesut Ozil makes it 2-0 with a tap-in after Krul brilliantly keeps out two efforts from Giroud at the near post.
45+2’ - SAVE! Great save from Krul to deny Cazorla from close range.
65’ - GOAL! (Arsenal 3-0 Newcastle): Giroud gets his 21st goal of the season, heading Ozil's cross to the near post past Krul. Nice little pass by Ramsey in the build-up to release the German.
87’ - CHANCE! Monreal gets in round the back but is denied by Krul, then Podolski's follow-up ends up on the roof of the net.
The Magpies have lost nine of their last 10 Premier League games at Arsenal.
Newcastle remain in the top-half of the table despite losing ten of their last 13 Premier League matches.
Will Pardew get the sack? Probably. Newcastle have been awful recently, and David Moyes is available...
MAN OF THE MATCH
Mesut Ozil (Arsenal): The German scored one and set up another with a superb performance in the middle of the park that brought back memories of his coruscating early season form. But a humdrum Monday night at home to Newcastle is one thing - Gunners’ fans will be looking for more from their 25-year-old playmaker in the big games next season.
Arsenal: Szczesny 7, Sagna 7, Mertesacker, 7 Koscielny 7, Monreal 7, Arteta 7, Ramsey 8, Ozil 9, Cazorla 8, Podolski 7, Giroud 7. Subs: Rosicky 7, Flamini 7,Sanogo 7.
Newcastle: Krul 7, Debuchy 6, Williamson 6, Coloccini 6, Dummett 6, Gosling 5, Anita 5, Tiote 6, Gouffran 6, Sissoko 6; Remy 6. Subs: Yanga-Mbiwa 6, Armstrong 6, Shola Ameobi 6.