The shadow of Paul Lambert is one Chris Hughton has struggled to emerge from since replacing the Scot as Norwich City manager but he can rightly feel a large step into the light has been taken following this victory, the team's first of the season and one that was fully deserved against opponents who were expected to triumph but looked short of ideas and energy throughout.

Grant Holt's 19th-minute close-range strike was all that separated the sides here but Norwich will feel that they deserved more for their efforts. Coming into this game having lost their past three matches, and suffering respective 5-2 and 4-1 thrashings to Liverpool and Chelsea in the most recent of those fixtures, the hosts could easily have cowered against another stellar name. Instead they grasped the initiative against Arsenal and were ultimately rewarded for an organised, resilient and smart display.

Few within the home ranks will feel as satisfied as Hughton, who has endured a tough time since arriving at Carrow Road. He took over at a club that had finished 12th on their return to the Premier League last season and, justifiably, were disappointed to see Lambert, the architect of that remarkable success, move to Aston Villa. Hughton led Norwich to just three points from their opening seven league games – the club's worst start to a top-flight season – but now they truly have lift-off, climbing out of the relegation zone to 15th place.

"The most satisfying thing is the three points," Hughton said. "It's been a long time coming, there have been performances that warranted it but this division is unforgiving and unless you're able to score more goals than the opposition then it doesn't come.

"If there was one disappointment it was that we could have made life a touch more easy for ourselves near the end of the game, but I'm pleased and delighted for the team – this is a win they deserved."

That was a sentiment shared by Arsène Wenger, who praised Norwich for their "focus and commitment" and accused his own team of "underestimating the difficulty" of their opponents. The visitors certainly appeared surprised by the quick, aggressive start made by Norwich and struggled thereafter to impose themselves. "It was a disappointing performance," said the Arsenal manager, whose side are now 10 points behind the leaders, Chelsea, after their second loss of the season. "We lacked sharpness and focus and only tried to get into the game after 20 minutes."

By that stage Norwich were in front, with Holt pouncing after Vito Mannone, the Arsenal goalkeeper, had failed to keep hold of Alex Tettey's long-range drive. It was the striker's third goal in his last three games and reward for a display of relentless commitment from the 31-year-old. In truth, desire was the hallmark of every player in yellow and green, with a defence that had conceded nine goals in their past two games well organised and the two midfielders in front of them, Tettey and Bradley Johnson, working constantly to restrict the space afforded to Arsenal's attacking trio of Lukas Podolski, Santi Cazorla and Gervinho. Ahead of them, Anthony Pilkington and Elliott Bennett were willing runners on the flanks while Wes Hoolahan operated with composure and craft in a position just behind Holt.

In contrast Arsenal were sluggish and disjointed, and despite dominating possession – 62% compared with Norwich's 38% – they created few chances. The best fell to Olivier Giroud early in the second half but, as has been typical of the French striker since his arrival from Montpellier, he made a mess of a close-range scissor kick following Carl Jenkinson's cross into the area.

Wenger may have been tempted to bring on Jack Wilshere, with the midfielder named among the substitutes after his recovery from an ankle operation that has kept the 20-year-old sidelined since June last year, but instead he turned to another English tyro, Alex Oxlade-Chamberlain, who, having come on in the 65th minute, had to be replaced by Andrey Arshavin nine minutes later after injuring his hip. The moment rather summed up Arsenal's evening.

In contrast, Norwich kept going and could have added a second goal late on when Holt found himself one-on-one with Mannone after a slip by Thomas Vermaelen, only to see his subsequent chip easily held by the Arsenal goalkeeper. Cue groans from an otherwise raucous home crowd. Ultimately, though, they were not to be denied a precious win.