Giroud opened the scoring with a classic centre-forwards goal on 15 minutes, burying an Alexis Sanchez cross.
Danny Welbeck had a goal disallowed before Cazorla doubled Arsenal’s lead with a cheeky finish on 54 minutes.
Two was soon three as Giroud cleverly flicked another right-wing cross - this time from Héctor Bellerín - into the net.
Ayoze Pérez pulled one back for Newcastle on 63 minutes but Cazorla grabbed his second from the penalty spot after Welbeck was fouled by Paul Dummett.
Arsenal started at a ferocious tempo and Per Mertesacker, who came in for criticism from Jamie Carragher for his performance in last weekend’s 3-2 defeat at Stoke, came close to opening the scoring when heading a Cazorla corner against the crossbar.
The early pressure from the hosts did finally tell on 15 minutes when Giroud and Sanchez linked up to brilliant effect.
Olivier Giroud rises highest to score the opening goal.
Sanchez found space on the right-flank before delivering a pin-point cross for Giroud, who rose above Daryl Janmaat and hammered a header into the top-corner.
Welbeck could have added a second minutes later but his goal from a tight angle was disallowed for a trip on Janmaat.
Newcastle had a penalty appeal of their own turned down on the half-hour mark when Welbeck handled the ball in the area before Mike Williamson and Papiss Cisse were both denied by the returning Wojciech Szczesny, who produced two point-blank saves to keep his side in front.
It turned out to be a very happy 30th birthday for Cazorla as he grabbed the first of his two goals on 54 minutes
Sanchez was once again the man with the assist as he found the Spaniard with a precise ball in the area.
The diminutive midfielder danced through a Fabricio Coloccini challenge and dinked the ball into the far corner.
Arsenal continued to press forward at pace with an obvious gameplan to target Dummett down the Newcastle left.
That ploy reaped more rewards four minutes later when the impressive Bellerin beat his marker down the flank and sent in a cross that was flicked home at the near post by Giroud, who has now scored six goals in five Premier League appearances against Newcastle.
The visitors did briefly threaten when Perez gave his side hope with a clever header that found the net following a Jack Colback centre but any hopes of another famous Toon comeback against Arsenal were dashed as Alan Pardew's men struggled to create clear cut chances.
It was Arsenal that looked the more likely scorers and after a chorus of “only one Arsene Wenger" rang around the Emirates, Cazorla grabbed a fourth with two minutes remaining from the penalty spot.
Welbeck was fouled by Dummett and Cazorla cheekily chipped the ball home - otherwise known as a “panenka” - to seal a victory that closed the gap between Arsenal and Manchester United in third to just two points.