Cardiff trailed to a thunderous effort from Marco Stiepermann at the break but turned the match around in the second half with a penalty from Joe Ralls and further goals from Junior Hoilett and Omar Bogle.
The win moved Cardiff up to 43 points, with Wolves visiting Birmingham City on Monday, while Aston Villa missed the chance to go third after a 1-1 draw at Leeds United.
Cardiff had looked in trouble at halftime following Stiepermann's effort from distance but whatever manager Neil Warnock said in the halftime interval produced a stirring reaction after the break.
Ralls, who also missed a penalty later in the game, levelled from the spot four minutes into the second half after Ivo Pinto was penalised for a shove in the box.
A looping finish from Hoilett then put them ahead with 25 minutes remaining and Bogle finished a cross from close range to wrap up victory on Warnock's 69th birthday, leaving Norwich winless in eight games.
Leeds went ahead when Pontus Jansson headed in at the near post after 19 minutes but Villa found a route back into the match after 71 when Henri Lansbury fired low into the net.
(Reporting by Toby Davis; Editing by Clare Fallon)
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