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Scott Rendell scored 10 minutes from time to earn the fifth-tier side a 1-0 win at Norwich's Carrow Road stadium and leave another indelible mark in the competition's giant-killing history.
Premier League Queens Park Rangers also suffered a humiliating 4-2 exit at the hands of third tier Milton Keynes Dons to pile on the misery for the struggling London club who are mired deep in a relegation battle.
Drama was in short supply at Stoke City, however, where Premier League champions Manchester City won courtesy of a late strike from Pablo Zabaleta and Arsenal substitute Theo Walcott scored in the 85th minute to edge his side past second-tier Brighton 3-2.
Everton's John Heitinga scored in the 90th minute as the Premier League side beat Bolton Wanderers 2-1.
Not since Sutton United beat Coventry City in the third round in January 1989, had a club from outside the top four divisions overcome top-flight opposition in the FA Cup.
Luton, relegated from the old first division in 1992 and dumped out of the Football League in 2009, lie sixth in the fifth tier of English football.
Norwich had made six changes from the team that lost 5-0 to Liverpool in the Premier League last week in a clear statement of where the competition ranked in the club's priorities.
For Luton, the occasion was a far cry from their last match, a 0-0 draw with Telford in the Blue Square Premier division.
The gap between the two sides, however, meant little as Luton held off a their opponents before striking late in the second half when Rendell steered home JJ O'Donnell's low cross.
"It's a lot to take in. The players were tremendous today," said Luton manager Paul Buckle, whose team beat second tier Wolverhampton Wanderers in the third round. "They held a Premier League team for 90-plus minutes.
"It's a huge day for them, for me and for our supporters. Norwich pushed us all the way but we were good for the win in the end. Scotty scored, it's what he does best, but everyone played their part."
The Premier League's bottom club QPR played a second-string team against MK Dons and were comprehensively outplayed by a side 31 places below them in English leagues.
QPR retained only two players from the side that drew 1-1 with West Ham United in the Premier League last Saturday, and were behind after four minutes when Armand Traore put through his own net.
Ryan Lowe latched on to a ball over the top and rifled home a second five minutes before the break, Ryan Harley made it three and Darren Potter profited from appalling QPR defending to fire home a fourth.
The hosts salvaged pride with late goals from Jay Bothroyd and Fabio, although the late rally did little to appease Rangers manager Harry Redknapp.
"It was bitterly disappointing, there is no excuse for conceding four goals at home to MK Dons. It was disgusting," Redknapp said.
Manchester City booked their place in the fifth round as Zabaleta scored a late winner with a neat finish to overcome an organised Stoke City.
City enjoyed the majority of the possession and created the best opportunities but could not find a chink in the home team's armour until the 85th minute when Zabaleta arrived late in the area to poke home at the far post.
"It's a massive win on a tough pitch and it's difficult to win here," Argentine full back Zabaleta told ITV.
"Today we were solid at the back, and up front we were very aggressive. The Stoke crowd push the team a lot and we knew it was going to be difficult for us."
Arsenal were taken the distance by Brighton, who twice came back from Olivier Giroud goals before conceding a decisive third to Walcott with five minutes remaining.
Elsewhere, Reading beat Sheffield United 4-0, Wigan won 1-0 away at minor league Macclesfield Town and Blackburn won 3-0 at Derby County.