Blue Square Premier Luton, 85 places lower in the football pyramid than their hosts, named 10 of the players which beat Wolves in the third round, but it was three substitutes who combined in the 80th minute as Rendell converted JJ O'Donnell's cross following Stuart Fleetwood's pass.
"It's unbelievable to score the winner in a cup tie like this," Rendell said. "It's an unbelievable feeling to come to a Premiership club like Norwich and turn them over. It's fantastic to be part of history. We were aware of it. It's been a fantastic day for everyone."
Goalkeeper Mark Tyler celebrated victory against his hometown club, 20 years after he was released by the Canaries as a schoolboy.
Twice Tyler made important saves - from Simeon Jackson in the first half and substitute Grant Holt in the second and the one time he was beaten ex-Hatter Leon Barnett's headed crashed off the post - but he was rarely troubled otherwise.
The 35-year-old said: "It's my job. The hard part was the emotional side, coming back here playing. It's where I started. This is where I wanted to be as a little boy playing football. To come back here, play, keep a clean sheet, means the absolute world to me and my family."
Manager Chris Hughton felt his Norwich side did not deserve to exit the competition, defended his decision to make six changes and bemoaned the missed chances which ultimately proved costly.
"A big shock," Hughton said. "You have to give Luton credit. They came here with a game plan, we found it very difficult to break them down.
"The good chances we did have we weren't able to put them away.
"We pushed and pushed and they caught us on a classic counter-attack. It was a poor goal for us to concede."
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- Mark Tyler