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.
Norwich manager Paul Lambert made four changes to the side which was beaten 1-0 at home by Leyton Orient in the FA Cup with captain Holt, goalkeeper John Ruddy and midfielders Andrew Crofts and Henri Lansbury, back after a hamstring injury, returning.
Former Canary favourite Craig Bellamy captained Cardiff on his first competitive return to Carrow Road since his departure in 2000.
The Bluebirds made a strong start and Peter Whittingham had an early effort from 25 yards saved by Ruddy.
They then took the lead in the seventh minute with a wonderful strike from Parkin, who lashed the ball past Ruddy from the edge of the box after linking up well with strike-partner Michael Chopra.
Norwich produced a positive response and after Russell Martin fired a shot wide, Fox saw his terrific 30-yard strike crash against the crossbar.
The home side continued to surge forward in their quest for an equaliser and Crofts' header was saved by Bluebirds goalkeeper Tom Heaton before the Canaries were denied a penalty in the 20th minute.
Holt went down under the challenge of Paul Quinn and, after Hampshire referee Keith Stroud waved play on, Wes Hoolahan saw his effort saved by Heaton.
Leon Barnett headed over a Fox free-kick before Cardiff came close to doubling their advantage but Bellamy, needing just one goal to reach 150 in his career, fired straight at Ruddy.
Norwich had the ball in the net in the 31st minute. Chris Martin`s 25-yard shot was parried by Heaton and Holt tapped the ball home only to be denied by the offside flag.
The Canaries began the second half as they finished the first - on top.
A deep cross from Drury found fellow full-back Russell Martin but he could not direct his 12-yard header on target.
Cardiff then had a great chance to stretch their lead in the 64th minute but Chopra was foiled by a fine save by Ruddy before Holt`s turn-and-shot was comfortably dealt with by Heaton.
Ruddy thwarted Chopra again as Cardiff tried to put the game to bed before substitute Aaron Wilbraham saw his 18-yard strike saved by Heaton.
He then lashed another strike over after Bluebirds substitute Chris Burke`s 25-yard free-kick was saved by Ruddy as the game switched from end to end, but Martin earned City a deserved share of the spoils.