Aaron Ramsey and Carl Jenkinson were the scorers on a final day of the Premier League season when there was little at stake at Carrow Road.
Both sides had known beforehand that only a series of freak scores would enable them to rise any higher in the table, with Arsenal beginning in fourth place and Norwich third from bottom.
Norwich’s cause was always going to be forlorn as they required not just West Bromwich Albion to lose at home to Stoke but also to win and be the beneficiaries of an incredible 17-goal swing.
Arsenal though required an even bigger turnaround to prise third place from Chelsea.
In the end both sets of supporters witnessed an afternoon of little drama, although Ramsey’s goal was particularly impressive, and Norwich ended their season three points adrift of safety.
Arsenal’s campaign will come to an end at Wembley next Saturday when they will look to beat Hull City and claim their first trophy since they won the FA Cup in 2005.
The starting line-up selected at Carrow Road by manager Arsene Wenger, who has insisted he will sign a new Arsenal contract soon, included five changes, most of which were defensive, but was nevertheless a strong side.
One of those changes, goalkeeper Lukasz Fabianski, pulled off a save at his near post to deny Nathan Redmond before Lukas Podolski fired a long-range shot wide at the other end.
Norwich goalkeeper John Ruddy then came out to make a good block of another Podolski effort but there was little urgency from either side in the opening half-hour.
Ruddy then pulled off an even better save to deny Olivier Giroud, who had been put through by Podolski as the Norwich defence napped.
The Frenchman soon had another go but again Ruddy made a top-quality save to boost his chances of going to the World Cup finals with England.
– Ramsey class –
The second half began with Podolski nodding over a corner from close range but with little at stake the German was able to laugh about it as he trotted downfield.
Ramsey improved the quality of proceedings with a top-quality strike to put Arsenal ahead in the 53rd minute.
Giroud picked him out at the back post with a chip from the left and the Wales midfielder volleyed into the top corner, giving Ruddy no chance.
Jenkinson made it 2-0 in the 62nd minute by being the first to react in the Norwich box when Podolski’s shot was half-blocked by a defender. It was the 22-year-old’s first Arsenal goal.
Arsenal immediately sent on Jack Wilshere for the England midfielder’s first appearance since suffering a broken foot while on international duty against Denmark at the start of March.
Abou Diaby also made his long-awaited comeback from injury, replacing Tomas Rosicky for the final quarter of an hour, with Giroud also replaced by Yaya Sanogo. Diaby had been missing for 14 months with a knee injury.
Sanogo almost squeezed in a late third goal but Ruddy was able to get a glove on it and divert the ball away.