The Gunners captain netted in the 27th and 60th minutes to record his fourth brace of the campaign to record the North London club's fifth win on the trot which moved them into to sixth place on the table level on points with Chelsea and Tottenham.
The opening goal came seemingly against the run of play 17 minutes in when Arsenal defender Per Mertesacker let a long ball from Marc Tierney run into the Norwich area only to see Steve Morison strip him after he was tracked by the Welshman who slotted neatly past Wojciech Szczesny for his third in three matches.
The Gunners were back on level terms ten minutes later when Theo Walcott beat Tierney down the right before playing in a low cross for Robin van Persie who calmly slotted home from the six-yard box as Gervinho missed his initial attempt.
Arsenal were made to work hard for their second which came just prior to the hour-mark when Aaron Ramsay won the ball in midfield for Alex Song who put it into the path of van Persie and the Dutchman gave his side the lead evaded John Ruddy with a deft chip on his right boot to make it 31 goals in 29 league outings in 2011.
Norwich maintained their never-say-die attitude after falling behind but Arsenal managed to snuff out their advances to make it six wins from their last seven league outings and inflicting a second defeat in a row on the Canaries.
Arsenal's Walcott could have been on the scoresheet in the 11th minute when his goalbound effort was kept out by defender Russell Martin's intervention and he was again a thorn in the Gunners side when Gervinho was clear on goal with the Canaries centre-half putting his boot through John Ruddy's initial save.
Early in the second half, Arsenal should have been ahead when van Persie crafted an inch-perfect through ball for Gervinho who rounded Ruddy but the Canaries keeper managed to come up with a brilliant save just as the Ivorian got his scuffed shot away whilst Norwich were inches away from a leveler when it was 2-1 when Elliott Bennett crossed to the front post for Anthony Pilkington who only needed a subtle touch to knock it past Szczesny but got less than what was required in what was a major let off for the visitors.
Overall, however, the Gunners were the better side on the day with plenty of scoring chances and in the end got the result that Arsene Wenger so desperately wanted as Paul Lambert's men remained in mid table after losing just their second match at home this season.
TRIBAL ASKS: Would Arsenal even be in the top half if it wasn't for van Persie?