With Arsenal's first choice stopper Wojciech Szczesny a long term injury victim, and his back up Lukasz Fabianski damaging ligaments in training during the week, Arsene Wenger once again turned to Mannone in goal, but the Italian's poor handling was decisive as Holt netted from the rebound to give Norwich their first Premier League win of the season.
Wenger's side are now 10 points behind leaders Chelsea as their spluttering start to the season continues, while Norwich climb out of the relegation zone thanks to their first win over Arsenal for 20 years.
Jack Wilshire was a welcome sight on the bench as the Arsenal midfielder returned for the first time in 17 months after a series of injuries, but Wenger opted not to send on the England international even with the game drifting away.
Anthony Pilkington caused early problems for Arsenal with a cross towards Holt, which was cleared by Per Mertesacker, and then went close with a 20-yard shot.
Moments later Norwich were on the back foot as Lukas Podolski flashed a left-footed shot across John Ruddy's goal.
But Arsenal struggled to find time and space to play their usually expansive football as Norwich harried them out of their rhythm.
The Canaries' confidence grew and they went ahead in the 19th minute when Mannone failed to hold on to a long range shot from Alex Tettey and Holt followed up to put away from inside the six-yard box.
It was Holt's third goal in as many games after netting against Liverpool and Chelsea after an early season drought.
Michael Turner came close to doubling Norwich's lead with a header from Pilkington's corner.
There were howls of derision from the home crowd when Gervinho made a complete hash of a ball dropping to him from a Mikel Arteta free kick as Arsenal began to look out of sorts approaching half-time.
Ruddy was made to work in the second half when he punched out a Carl Jenkinson cross, which fell to Olivier Giroud but was unable to get a clean connection on an attempted shot 10 yards out.
A weak Gervinho header failed to trouble Ruddy after Aaron Ramsey and Giroud combined.
Wes Hoolahan put the ball in the net for Norwich nine minutes after the break but the offside flag was already up.
Norwich then had a penalty claim turned down by referee Lee Probert when they felt Arsenal captain Thomas Vermaelen handled a Pilkington cross.
Carl Jenkinson made a stunning block to thwart Holt and Bradley Johnson did the same to deny Santi Cazorla at the other end as the final whistle approached.
Wenger's problems deepened when substitute Alex Oxlade-Chamberlian, who had replaced Podolski, had to come off with a knock after just nine minutes with Andre Ashavin going on.
With Arsenal committed to attack they were almost caught on the break by Holt who burst clear but shot wide.
The Norwich skipper had an even better chance when he took advantage of a Vermaelen slip and fluffed his finish in a one-on-one with Mannone.