Blue Square Premier Luton, 85 places lower in the football pyramid than their hosts, named 10 of the players who beat Wolverhampton Wanderers in the third round but it was three substitutes who combined in the 80th minute as Rendell scored.
The 1-0 victory saw top-flight opposition beaten by a side outside the Football League for the first time in 24 years and the first time in the Premier League era.
And Rendell said: "It's unbelievable to score the winner in a cup tie like this. 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 about today 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. The boys have done brilliantly in front of me, limited them to two chances.
"We countered in the second half and the subs made the impact and it was a great finish."
Rendell knew little about his goal, which will live long in the memory of the 4,000 travelling fans, although Nick Owen, the Luton chairman, was not among them. Instead the broadcaster was on holiday.
Rendell said: "I didn't see it go past the goalkeeper. I just heard a big roar. I've never had a feeling like it."