"He was brilliant again today, got two good goals and set Laurent's goal up as well. Hopefully it continues for him because he's having a great season and his confidence is brimming and that helps the team as well."
The victory may have come at a cost. Defender Mathieu Debuchy, who had only just returned from an ankle problem, was carried off during the first half with a shoulder injury sustained when falling into the advertising hoardings after colliding with Stoke's Marko Arnautovic.
Arsenal goalkeeper Wojciech Szczesny, meanwhile, had been left to watch from the bench as David Ospina made his Premier League debut. It came after a week of negative headlines for Szczesny over smoking in the showers after the loss at Southampton on New Year's Day.
But it was a quiet day for Ospina on a day when Arsenal was in complete control.
Arsenal had shown its intent from kick off as Sanchez tested Begovic with an early effort which was curling towards the bottom right corner before being pushed behind.
Stoke has not won at Arsenal since 1981 and was soon behind. Begovic pushed an angled drive from Rosicky behind. Sanchez's corner was only half-cleared, and Koscielny played the loose ball back out to the forward. Koscielny ran off into the six-yard box and ghosted in unmarked to plant a firm header past Begovic from Sanchez's cross.
Arsenal continued its offensive, with Oxlade-Chamberlain shooting wide after being played in on the right by Sanchez.
Olivier Giroud " back from a three-match suspension " was denied by a spectacular flying save, but Begovic couldn't keep out Sanchez's strike.
A quick exchange with Rosicky put Sanchez in space on the right. He jumped the lunging challenge of Steven Nzonzi before darting into the penalty area, where he turned Stoke captain Ryan Shawcross inside-out before clipping the ball past Begovic inside the goalkeeper's near post.
Begovic was beaten again at the start of the second half.
Steve Sidwell tripped Oxlade-Chamberlain on the edge of the penalty area. Sanchez's low free-kick took a deflection off Stoke defender Geoff Cameron in the wall which deceived Begovic, who could only push the ball against the post before it squirmed over the line.
Arsenal went close again when Santi Cazorla shaved the crossbar with an angled chip. Theo Walcott and playmaker Mesut Ozil, who returned after three months out with a knee injury, also shot wide.
At the Emirates Stadium some fans brought signs emblazoned with "Je Suis Charlie" (I am Charlie), the phrase adopted as a tribute to Wednesday's deadly attack on French satirical magazine Charlie Hebdo, which started three days of terror around Paris.
