Norwich made a stunning start to silence the Wednesday hordes, with Huckerby, who might not be at Carrow Road next season, combining with Dion Dublin in the eighth minute to slice open the home defence.
Norwich had chances to increase their lead, but out of the blue the Owls were handed a lifeline.
Burton and Jason Shackell challenged for a ball over the top and referee Mark Clattenburg had no hesitation in awarding a penalty when the Owls striker went tumbling just inside the box
Burton held his nerve to convert the penalty and Wednesday looked much more assured after the break.
Dublin was given a standing ovation to mark the end of his 20-year career when he was replaced by Jamie Cureton with 25 minutes left.
Norwich boss Glenn Roeder was full of praise for the departing 39-year-old.
"He's had a brilliant career, he's a top human being, and everything that Dion Dublin has got out of life so far he deserves," said Roeder. "Hopefully there's plenty of good times left for him in retirement."
Wednesday boss Brian Laws: "Under the circumstances, and I'm not patting myself on the back, but if Mourinho was here I don't think he could have done any better.
"We've had everything thrown at us and yet everybody has stayed calm and very focused. We never threw in the towel." More Laws quotes
Norwich boss Glenn Roeder: "The players have been left in no doubt as to how angry I am.
"Some of them need to look at themselves to see if they have a future here next year.
"It was totally unacceptable. It was the Norwich I don't want and I won't have."
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