Scott Rendell's 80th minute goal earned the club from English football's fifth tier a 1-0 victory to steal the fourth round limelight and add their name to the list of the competition's most notable giant-killings.
Not since 1989, when Sutton United beat 1987 FA Cup winners Coventry City, have a side from outside the Football League beaten a top flight side.
Luton's achievement is more impressive given the financial muscle now wielded by the Premier League compared to the fraying shoestring budgets the likes of Luton live on.
Manager Paul Buckle said he hoped Saturday's win could be the catalyst for a return from the football wilderness for the club known as the Hatters.
"If there's one thing about today that I want the players to take away, its belief. Belief that they can achieve something special," Buckle told the BBC.
""You need great belief and we had that today. It's a lot to take in. The players were tremendous today. They held a Premier League team for 90-plus minutes.
"It's a huge day for them, for me and for our supporters."
Despite their current lowly standing, it was not so long ago that Luton were themselves members of the country's elite, having spent a decade in the top flight after gaining promotion under the enlightened coaching methods of David Pleat in 1982.
Always a forward-thinking club, Luton discovered black talents such as Ricky Hill and Brian Stein, were one of the first clubs to experiment with a plastic pitch and took a leading role against hooliganism in the 1980s, banning away fans after Millwall supporters rioted at Kenilworth Road.
Even their orange kit used to be something of a novelty while their stadium was instantly recognisable by what appeared to be a series of conservatories running down one side.
However, after being relegated in 1992 the club began a relentless drift down the divisions.
A brief revival saw them climb from the fourth tier to the second tier in 2005 before a financial meltdown resulted in a spiral that saw them exit the Football League in 2009 after suffering a 30-point deduction.
Stability has since returned for the Hatters but three consecutive play-off defeats have been a bitter pill to swallow as they try and regain their place in the Football League.
"We are good enough to play in the Football League, we just need to get out of the Conference," Buckle said.
"Getting back in the league is the main priority for us but, for me as a manager, this win today is right up there."
Sadly for the club's chairman, former TV presenter Nick Owen, he was not around to witness Luton's most memorable day since he led a consortium to buy the club in 2008.
Owen was enjoying a Caribbean cruise as news of Luton's victory over Norwich filtered through.
"I'm going absolutely bonkers here," he told the BBC.
"I had my three sons at the game and they were keeping me up-to-date. I couldn't believe it when the goal went it. It is one of the great days in the club's history."