The Canaries registered their first Premier League win of the season as Arsene Wenger's side failed to create clear-cut chances despite dominating possession at Carrow Road
The Gunners had more possession throughout, but the host opened the scoring through Grant Holt in the first half after Vito Mannone spilled a long-range shot.
The Canaries were forced to hold on for periods of the match, but a solid defensive performance saw them hard to break down, with the visiting side creating few clear-cut chances.
Norwich made two changes from the side that was swept aside by Chelsea two weeks ago with Leon Barnett being replaced by summer signing Michael Turner, while Anthony Pilkington came in for Jonny Howson, who dropped to the bench.
Arsenal came into the match in good form and made just the one change to the side that beat West Ham away last time out, with Andre Santos starting at left back in place of the injured Kieran Gibbs.
Jack Wilshere was named among the Gunners' substitutes, despite Arsene Wenger's claims that the midfielder, who has missed 14 months due to injury, was still weeks away from a return.
The host came out of the trap in a determined manner, with Pilkington going close early on, but the Gunners soon took control of possession, making the match look like a training session at times, yet they could not create clear opportunities.
Norwich’s steely rearguard action was providing an excellent launch pad, and it was soon in the lead, with the help of Arsenal goalkeeper Mannone.
Bradley Johnson cut the ball back to Alexander Tettey about 25 yards out, and the Norwegian tried his luck, only for his effort to be spilled by Mannone but Holt was rushing in and buried the rebound.
The goal saw Norwich showing significantly more on the ball, and although Arsenal generally continued to edge the possession, it was the host which went close next, but Turner, who was booed before kick-off, headed a great chance wide after Wes Hoolahan’s corner and the Canaries went into the break in the lead.
After the break, the match followed a similar pattern to what had been established in the first half, with Norwich doing most of the running about, while the Gunners stroked the ball around with little end product.
Olivier Giroud was presented with an opportunity to get a shot in when John Ruddy punched Carl Jenkinson’s cross straight to him, but his effort bobbled harmlessly wide as Arsenal pressed hard for an equalizer.
With 20 minutes to go, Thomas Vermaelen presented Norwich with an excellent chance to secure the win after slipping on the halfway line, but Holt’s attempted chip went straight into the hands of Mannone.
Arsenal piled the pressure on in the final ten minutes, but they still could not break down the Norwich defense that held strong, with Leon Barnett's last-ditch block on Gervinho securing the win.
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