Throughout the contest at Carrow Road, there was little evidence of the 85 football pyramid places separating Paul Buckle's Blue Square Premier side and their star-studded hosts.
And, in the 80th minute, substitute striker Rendell scored what proved to be the winner to ensure Luton became the first non-league side to win at top-flight opposition in 27 years.
Luton had been cheered on by 4,000 travelling fans and they will make the trip home for a major celebration after their side became just the seventh non-league team to reach the fifth round since World War II.
Norwich were booed off and will be keen to forget their display, with immediate attentions turning to Wednesday's Premier League meeting with Tottenham Hotspur, while for Luton, who last beat top-flight opposition in 1994, the match will live long in the memory.
The 1959 finalists and 1994 semi-finalists were seeking to revive former glories in their first meeting with Norwich in six years - a match which came as the Hatters were tumbling down the divisions and the Canaries were preparing for a revival.
Six changes were made by Norwich, with Declan Rudd, Andrew Surman, David Fox, Elliott Bennett, Simeon Jackson and Harry Kane given a chance to impress as Luton named 10 of the players which beat Wolverhampton Wanderers in the third round.
Rather than take the initiative, Norwich were drawn into a scrappy battle as Buckle's Luton set about their task well.
The home team were guilty of missing chances and an initial header by Russell Martin was met by Leon Barnett, who bulldozed in to meet the ball above goalkeeper Mark Tyler, who was released by Norwich as a 15-year-old, but it crashed off the post and was scrambled clear by Alex Lawless.
Kane was replaced at half-time by Grant Holt, who took the captain's armband from Martin and provided a presence up front Norwich had lacked in the opening 45 minutes.
But Chris Hughton's side still lacked a cutting edge and, with 17 minutes remaining, Wes Hoolahan and Anthony Pilkington replaced Surman and Elliott Bennett.
Pilkington headed over Javier Garrido's cross from the left before Norwich were caught napping at the other end and nearly punished when Lawless steered the ball narrowly wide.
Moments later the Luton took the lead with a devastating move down the left as three substitutes combined.
Stuart Fleetwood freed JJ O'Donnell down the flank, he reached the byline and cut the ball across and Rendell nipped in front of Ryan Bennett to direct the ball into the top corner.
Norwich never looked like finding an equaliser and hopeful shouts for a penalty when the ball bounced off Lathaniel Rowe-Turner's thigh and onto his arm were in vain as Luton claimed a famous win.