Scott Rendell's 80th-minute strike earned the Hatters, who have spent much of the last 20 years battling oblivion and financial woes, a 1-0 victory at Carrow Road against a side 85 places above them in the football pyramid.
The 1959 finalists and 1994 semi-finalists emulated Sutton, who in 1989 beat top-flight Coventry.
Luton now reside in the Blue Square Premier, yet, after a third-round defeat of Wolves and the victory over Norwich, Buckle believes his players are suited to playing on the big occasion.
"I feel we can play on this sort of stage," Buckle (above) said. "A brilliant pitch every week it would make life a lot easier. On a good surface on a good day like this you can get your point across. I knew what Norwich were going to do; move the ball, trying to open us up. Sometimes when you play on a poor pitch it can be a real leveller. The last three or four have been impossible to play any football; it's been a fight."
After tumbling down the divisions and exiting the Football League, Luton are targeting a return. At sixth in the Blue Square Premier, Buckle believes they are firmly in contention.
"We are desperate to play in the league and we bought a lot of league players who can really raise their game for this type of tie," the former Torquay and Bristol Rovers boss said.
After seven losses in 10 games Norwich must prove once more that they are a good side.
The Luton loss came just a week after a 5-0 defeat at Liverpool which extended the winless league run to six matches.
The addition of a striker, be it Celtic's Gary Hooper or Sporting Lisbon's Ricky van Wolfswinkel, would be welcome, but time is running out as the transfer window comes to a close.
"We've been endeavouring to do that," Norwich boss Chris Hughton said. "People on the outside think it's very easy to bring in the players you want. It doesn't work that way."