Aaron Ramsey bagged two and Mathieu Flamini scored the other at the Cardiff City Stadium.
In a strong Arsenal start, Wilshere almost got the match off to an emphatic start within 30 seconds, curling an excellent strike against the bar from the edge of the area.
However it was Cardiff that went on to have the next big chance. Per Mertesacker was off the pitch following a clash of heads, and while he was absent Frazier Campbell met a rightwing cross with a downward header than went just wide.
Aside from that chance the away team were looking very comfortable, pinning Cardiff back and having plenty of possession 30 yards from David Marshall's goal.
There was a crazy moment around the twenty minute mark as Frenchman Olivier Giroud burst through on to a forward pass, alongside Mesut Ozil who had flicked out a leg to help it on. The ball eventually made its way to the striker who by then was miles offside and assumed the whistle would go. The linesman never signalled though, and after two or three seconds of his teammates telling him to shoot on goal, the Cardiff defence got back in place and Giroud's belated shot was deflected away. Video replays showed that Ozil had in fact touched the ball on when Giroud was yards beyond the last man. The officials would have been relieved that Giroud hadn't found the back of the net as it would have been as a result of a terrible decision.
However Arsenal didn't have to wait long to score, and they didn't need the help of a dodgy decision. In the 29th minute, Ozil whipped the ball from deep towards the penalty spot, finding Aaron Ramsey on the end of a great run with a powerful header that flew into the top right corner. It was an outstanding finish and the Welshman's refusal to celebrate against his former club impressed both the home and away fans.
Cardiff were sitting too deep though may have done better from a couple of loose balls and free kicks that they didn't manage to make the most of.
Just before half time Ramsey nearly scored a second after sloppy play from Ben Turner, but after taking down Giroud's ball in the box the Arsenal midfielder couldn't find the target.
The second half continued in dominant fashion for Arsenal, Ramsey again looking dangerous as he burst into the box and cut back to Giroud, only for the foward's shot to be cleared off the line by Turner.
And despite struggling to deal with Arsenal for much of the game, Cardiff nearly equalised on the 50 minute mark, when another great header from Campbell drew a Gordan Banks-esque save from Wojciech Szczesny down to his right.
It was a fantastic stop and seemed to ignite an encounter that had been vastly one-side beforehand.
Cardiff were pushing forward much more and getting in Arsenal's faces as the half went on.
Clear cut chances for either team were hard to come by despite the game becoming more of a contest. Peter Whittingham volleyed straight at Szczesny from the edge of the box, as did Don Cowie a few minutes later.
With the next goal promising to be key, Arsenal took advantage as Cardiff left gaps at the back late on, and with five minutes to go Mesut Ozil found substitute Mathieu Flamini to sweep home for his first goal since returning to North London.
And Arsenal found a third in injury time, Ramsey blasting home again from inside the box following a counter attack. It was a little cruel on the home team but Arsenal were comfortably on top throughout.
A last minute equaliser seemed a long way away for Cardiff this week, and in preventing such a thing Arsenal proved just how far ahead they are of last season's champions, and the rest of the Premier League.