The Canaries recorded their first league win under new boss Chris Hughton after producing a hard-working display to capitalise on a lacklustre performance by the Gunners.
Holt reacted quickest after stand-in goalkeeper Vito Mannone had spilled Alex Tettey's 25-yard effort midway through the first half to slot his third goal in successive games.
Despite having plenty of possession Arsenal failed to stretch the hosts, who could have gone into the break with a two-goal cushion had defender Michael Turner not planted his close-range header wide from a corner.
After suffering heavy defeats to Liverpool and Chelsea, Holt feels Saturday's performance was the perfect tonic for the battles ahead, which continue at Aston Villa next weekend and former manager Paul Lambert.
"Everyone had been looking at the negatives from the games against Liverpool and Chelsea, but we had played well in those matches," Holt said on Canaries Player.
"It is all about hard work and we have been putting the same endeavour in but not getting the rewards. We will take a lot from this result.
"No-one will have given us a chance of winning this and wrote us off too easily.
"We needed it and it has taken a while for us to wait for the performance and the win.
"We have to realise that is the only way we are going to get results in this division. If we keep doing it, then we will be all right."
Norwich had not beaten Arsenal at home since Boxing Day, 1984.
However, Hughton knows all the hard work will count for nothing if his side fail to follow it up.
"It is about levels of consistency," the former Newcastle and Birmingham boss said.
"We can talk well about what the team have done against Arsenal, but because of where we are we realise it is going to be a tough season so we know we have to show that level in more games than not.
"You have always got to try to get the balance right. On the back of a poor defeat last game you have then got to pick them up, and with this group it has not been so difficult.
"We accept we are not going to be in the top 10 and every game is going to be tough, but if we do it right then we have definitely got enough quality to do well enough."
Wes Hoolahan impressed in his forward role just behind Holt, watched by Republic of Ireland manager Giovanni Trapattoni.
Hughton was capped 53 times by the Republic, playing at Euro 88 and being part of the 1990 World Cup squad, and knows just what ex-Shelbourne man Hoolahan, 30, can give a side.
"Wes is a super player," he said. "But I would think that it would not just take this performance for Trapattoni to be aware of that because of what Wes has done over the past few seasons.
"But if he needed any clarification of that, he will have got that."