Frenchman Giroud this week came out in defence of his under-fire manager, who was on the receiving end of public vitriol from the club's fans in the wake of their 3-2 loss to Stoke City last weekend.
A 4-1 UEFA Champions League victory against Galatasaray in midweek went some way towards silencing the doubters, and Arsenal duly carried that momentum into Saturday's Premier League clash to record a resounding win.
Newcastle went into the match having lost just one of their last 10 in all competitions but they rarely looked like extending that run at the Emirates Stadium.
Giroud opened the scoring in the 15th minute with a precise header, before Spain midfielder Cazorla - celebrating his 30th birthday - doubled the advantage nine minutes after half-time.
Former Montpellier man Giroud effectively made the game safe four minutes later by turning home Hector Bellerin's low cross, rendering Ayoze Perez's 63rd-minute effort nothing more than a consolation.
Cazorla then added a fourth from the penalty spot with two minutes left as Arsenal moved to within two points of the top four.
Aside from the response to some Arsenal fans' public lambasting of their boss after that Stoke clash, the build-up had been dominated by Wenger's decision to deploy former Newcastle right-back Mathieu Debuchy in central defence following an injury crisis.
But it was the France international's centre-back partner, Per Mertesacker, who went close to opening the scoring in the eighth minute. His header from Cazorla's corner cannoned off the crossbar with Jak Alnwick well beaten.
Third-choice goalkeeper Alnwick was making his first start for Newcastle having come on for the injured Rob Elliot in last weekend's 2-1 win over Chelsea and, just seven minutes after Mertesacker's chance, the 21-year-old was picking the ball out of the net.
Giroud rose highest to meet Alexis Sanchez's cross and power the ball home with a well-directed header.
Arsenal were controversially denied a second by referee Lee Mason shortly afterwards. Danny Welbeck cut in from the left and cleverly lofted the ball over Alnwick, but Mason ruled that the former Manchester United striker had fouled Daryl Janmaat in the build-up.
Welbeck then volleyed wide from Alexis' superb chipped pass before appearing to handle the ball in the area at the other end.
Newcastle's claims for a penalty were dismissed, but the visitors would still have levelled in the 34th minute had it not been for a fine double save from Wojciech Szczesny to deny Yoan Gouffran and Papiss Cisse.
Mason drew the ire of Arsenal's players after 38 minutes for awarding a free-kick for Paul Dummett's foul on Alexis, even though the contact looked to have occurred inside the box.
Yet Arsenal's indignation at that decision was shortlived, Cazorla latching on to Alexis' pass to exquisitely lift the ball over a sliding Fabricio Coloccini before firing past Alnwick at his right-hand post.
Newcastle's defence, depleted by the suspension of centre-half Steven Taylor, struggled to live with the creativity and speed of the Arsenal attack, which was rewarded again when Giroud flicked in Bellerin's low ball across the face of goal.
A rout looked to be on at that point, only for Perez to glance home Colback's free-kick and give Newcastle a glimmer of hope with his fourth goal of the season after 63 minutes.
However, Arsenal were ultimately comfortable in seeing the game out, with the home fans serenading Wenger with supportive chants before Cazorla's delicately chipped spot-kick after Dummett had clumsily felled Welbeck.
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