The Bluebirds held out for a deserved victory in a pulsating match at Ninian Park.
First-half goals from Paul Parry and Robert Earnshaw gave Cardiff a huge lift after Norwich had applied all the early pressure.
They pulled one back through Leon McKenzie in the 54th minute but Cardiff held on to earn all three points.
"That was a massive scalp for us" said Bluebirds boss Lennie Lawrence.
"What pleased me most was that we had to grind it out at the end and that is something we haven't been able to do in a number of matches.
"They're a strong team who started well but we didn't fold and it was a tremendous victory.
"We were helped in the last ten minutes by the crowd getting behind us and they certainly assisted us as the game drew to a close.
"What is also pleasing is that we have managed it without three regular first-team players and to get a result like that speaks volumes for the strength or our squad."Cardiff were up against it from the first whistle but they went ahead with a bizarre goal. It was a first in league football for Parry who two months ago was playing in the Conference with Hereford United.
His cross, which was intended for Earnshaw, curled in at the far post with the Norwich keeper stranded.
Two minutes later the Bluebirds doubled their lead when Parry sent Alan Lee free down the left flank. His low cross was rifled into the net by Earnshaw - his 24th goal of the season.
Norwich changed formation in the second half and it paid off when McKenzie took advantage of a mistake by Tony Vidmar to reduce the deficit.
Both sides went close in the final quarter but the Bluebirds held on for victory.
Canaries boss Nigel Worthington thought that his defence had let him down particularly during the first period.
"Our defending was weak and when you defend like that you will be punished," he said.
"We pulled a goal back at the right time and pushed on with our attacking formation but just couldn't do it."