The Dutchman recorded his 30th and 31st goals of 2011, to leave his side unbeaten in eight games, after Steve Morison's early strike for the Canaries threatened to cause an upset.
Arsenal recorded its fifth straight win thanks to a Robin van Persie brace, helping his side to a 2-1 win against Norwich on Saturday.
Arsenal’s visit to Carrow Road was the first of any of the supposed ‘top four’ since Norwich were last in the Premier League, six years ago.
A sun-drenched Carrow Road saw the visitors make a lively start to the game, with the pace of Theo Walcott and Gervinho in the wide areas causing the Canaries problems.
The in-form Van Persie was also looking menacing in the early stages, dragging his 20 yard effort just inches past John Ruddy’s far post.
With just 10 minutes gone the visitors were left wondering how an earth they hadn’t taken the lead.
Following persistent play from Gervinho, Walcott received the ball 15 yards from goal. The winger cut inside onto his left foot, before curling a brilliant effort into the far corner, only for Russell Martin to defy the England man with a superb hooked clearance.
As so often is the case, Arsenal was left to rue its missed chances as Norwich took the lead just minutes later.
Summer signing Per Mertesacker was hassled by Steve Morison on the edge of the Arsenal area, and the forward’s pressure paid off as the German center back crumbled, leaving Morison one on one with Szczesny, before coolly slotting home.
The goal didn’t deter the visitors, as they continued in the same attacking fashion. Next it was Gervinho who was thwarted, as his low effort was blocked by John Ruddy.
They did, however, eventually get the goal their play deserved.
Unsurprisingly it was Walcott who created the goal, driving to the by-line before pulling the ball back for Van Persie, who was left with the simple task of restoring parity for his side. The goal was the Dutchman’s 14th in his last 17 games.
Just before the hour, Arsene Wenger’s men really should have taken lead for the first time in the game.
As so often, Van Persie was the linchpin in the attack, displaying some brilliant footwork, before threading the ball through for Gervinho.
The Ivorian side stepped the onrushing John Ruddy, and with the hard work done and an empty net gaping, he contrived to fire the ball at the diving Ruddy.
After seeing his teammates squander multiple chances, Van Persie took matters into his own hands and gave his side the lead.
Russell Martin, who hadn’t put a foot wrong all game, was caught in possession in the center circle by Aaron Ramsey. The ball fell for Alex Song, who slid Van Persie through, and the Dutchman did the rest, superbly chipping the ball over John Ruddy with his supposed ‘weaker’ right foot.
From then on it was an Arsenal master class, frustrating the home side with some excellent keep-ball.
The Canaries continued to search for an equalizer, but the late onslaught, which the Carrow Road faithful have become so accustomed to, did not materialize.
The win leaves Norwich in ninth, while Arsenal moves up a place to fifth, level on points with London rivals Chelsea and Tottenham.