The Gunners capitalised on Liverpool's draw at Newcastle with what proved to be a hard-earned victory over a determined Norwich side, who could consider themselves unfortunate not to take something from the match despite the final scoreline.
In the end, though, it was Arsenal's class which told, as Wilshere opened the scoring with a sublime finish to a slick passing move which had cut Norwich open on 18 minutes.
After soaking up plenty of pressure, Germany playmaker Mesut Ozil headed in a second just before the hour, but Jonny Howson reduced the deficit.
Arsenal, though, made sure there would be no late drama when Aaron Ramsey, who has started on the bench, fired past John Ruddy from close range after jinking into the six-yard box.
Ozil stroked in a late fourth to ensure a somewhat flattering scoreline, but it was more evidence this Arsenal side look set for a long-overdue sustained title challenge in 2014.
As expected, Arsenal made a bright start, with a low shot from fit-again Santi Cazorla saved by goalkeeper Ruddy, one of several players hopeful of impressing watching England manager Roy Hodgson.
Norwich, who has lost four of their opening seven Premier League games to sit in the bottom three, were without club-record signing Ricky van Wolfswinkel, who had been struggling with a toe injury.
Nevertheless, the Canaries looked to be in a positive mindset with Scotland winger Robert Snodgrass, who scored against Croatia and recently became a father, the main outlet down the right.
Arsenal, though, swept into the lead on 18 minutes with a goal of the highest order.
Norwich had plenty of men behind the ball as Cazorla pressed at the edge of the penalty area.
It did not matter, however, as a sublime series of one-touch passes simply cut through the yellow shirts like butter.
First Cazorla pulled the ball back out to Wilshere, who played a quick pass into Giroud. His return pass was then flicked straight back by the England man, and in turn touched forwards by the France striker into Wilshere's path as he carried onto to the six-yard box before clipping a low first-time shot past Ruddy.
There was a stoppage just after the half-hour following what looked a nasty clash of heads between Mathieu Flamini and Alex Tettey, but both men were soon back up on their feet.
Ruddy denied Giroud with a brilliant reflex save at his near post following a run and cross down the left by Kieran Gibbs.
On 38 minutes, Flamini was replaced by Ramsey, the French midfielder still feeling the after effects of his clash with Tettey.
A looping cross from Norwich defender Russell Martin's was palmed away by Wojciech Szczesny, who had been a spectator up to now.
The Poland goalkeeper, who played well at Wembley despite the 2-0 defeat by England, was tested again by a low 20-yard effort from Leroy Fer.
Norwich had another good chance at the start of the second half when a deep free-kick was headed back by Michael Turner to Martin. However, the Scotland defender sliced the ball horribly wide from 15 yards.
Arsenal, though, looked to have settled matters with another goal of high quality.
After soaking up plenty of Norwich pressure, the home side broke with devastating consequences on 58 minutes.
Cazorla sprinted into the opposition half before he fed Giroud on the right. The France international looked up and chipped a perfectly-weighted ball across the Norwich penalty area, where Ozil arrived on queue to get in between the defenders and glance a header into the far corner.
Nevertheless, the Canaries still refused to go away and their industry was rewarded with 20 minutes left when Howson drove the ball in at the far post after Martin Olsson's left-wing cross was only half cleared.
Arsenal clearly needed a third to finally kill off the game.
Ruddy saved a 20-yard thunderbolt from Ramsey before the England squad keeper then denied substitute Nicklas Bendtner.
Ramsey settled any late nerves when he cut into the six-yard box and fired past Ruddy, who was beaten again two minutes from time by Ozil's tap-in from a cutback by the Wales midfielder at the far post.
Source: PA
Source: PA