The full-back rifled the ball home via the crossbar following a stunning delivery across the face of the six-yard box by Adam Drury for the Canaries' sixth injury-time strike this season.
It seemed John Parkin would mark his debut with the only goal as Cardiff attempted to end a four-game losing run on their travels.
The giant striker fired the Bluebirds ahead in the seventh minute, lashing the ball home from 25 yards.
Norwich then hit the crossbar through David Fox, had a penalty turned down and saw a Grant Holt strike disallowed for offside before half-time.
The home side continued to pile on the pressure in the second half and just when it seemed they would suffer only their second defeat in 12 matches, Martin struck.
Source: PA
Source: PA