Martin fired City ahead in the 10th minute - his first goal at home - to secure a fifth win in six games in front of a crowd of more than 26,000.
QPR had defender Matthew Connolly sent off after 51 minutes for a professional foul on City captain Grant Holt.
But, after the Canaries wasted several chances to kill the game off, substitute Patrick Agyemang headed against the post with 16 minutes left before being denied by goalkeeper John Ruddy at the death.
Norwich, though, held on to post their first clean sheet in 11 games and climb to third in the table.
After Jamie Mackie headed an Adel Taarabt cross wide, the home side took the lead after 10 minutes.
A mazy run from Chris Martin resulted in his shot being blocked by Kaspars Gorkss but Russell Martin fired home the loose ball.
QPR, with just one win from their last seven away games, nearly produced an immediate response but Ruddy pulled off a stunning save to keep out Heidar Helguson's 12-yard drive.
New signing Aaron Wilbraham, who volleyed a shot wide from 12 yards in the 17th minute, was denied a debut goal by the linesman's flag moments after Helguson had fired his 20-yard effort off target.
Norwich then enjoyed a bit of pressure but Andrew Crofts and Holt were off target with efforts outside the box
Gorkss drilled a shot harmlessly over from long-range while Holt then had a header saved by visiting goalkeeper Paddy Kenny before dragging another effort wide following a nice counter-attack just before half-time.
QPR made a double change at the break with Bradley Orr and Agyemang replacing Clint Hill and Helguson.
But they suffered a further setback six minutes into the second half when Connolly was sent off for hauling down Holt.
From the resulting free-kick, Kenny parried Chris Martin's effort before QPR scrambled the ball clear.
Martin flashed another effort just wide as City looked for a second.
Taarabt, QPR's 11-goal leading scorer, was substituted on the hour and five minutes later Chris Martin wasted a glorious chance to double City's lead.
Wes Hoolahan, the hat-trick hero in Tuesday's 4-2 home win over Sheffield United, played in Martin with just Kenny to beat but the stopper saved well to keep his side in the game.
With Norwich failing to kill off the game despite dominating possession, Agyemang nearly stunned them when he headed against the post with 16 minutes left.
Hoolahan and Chris Martin also had opportunities to put the game to bed but Ruddy foiled Agyemang near the end.