Martin was denied by an excellent save from Tim Krul in the 13th minute but made the most of a tap-in to score seven minutes before half-time.
Wes Hoolahan pounced on a poor pass from Ryan Taylor, waltzed through the Magpies defence and squared the ball to Martin to roll into an empty net.
The Magpies came close to levelling in the 41st minute but Nile Ranger's strike was ruled out for offside.
But United equalise two minutes after the break when substitute Shola Ameobi slotted the ball through John Ruddy's legs from Xisco's pass.
Simeon Jackson was denied his first goal for Norwich when he was ruled offside in the 57th minute before Martin headed home a cross from Anthony McNamee with 15 minutes left.
In the 89th minute Peter Lovenkrands headed Shane Ferguson's cross against the crossbar.
For the record - Delia Smith did not appear on the pitch at half-time to rally the Norwich fans with either "I'm drunk, I'm drunk you silly old skunk" or "Let's be 'aven you!"
BUT ... three bottles of cooking sherry DID go missing from behind the bar.
CSI are on the case.
NORWICH CITY: Ruddy; R Martin, Nelson, Ward (Francomb 63), Drury; Crofts, Fox (Gill 78), Surman (Lappin 78); Hoolahan (McNamee 72); Jackson (Johnson 63), C Martin. Subs not used: Steer, McNamee, Dawkin, Tudur Jones.
NEWCASTLE UTD: Krul; Taylor (Routledge 45), Tavernier, Coloccini (Williamson 45), Diaz (Ferguson 57); Ranger (Xisco 45), Barton (Smith 45), Nolan (Guthrie 45), Vuckic (Edmundsson 72); Best (Lovenkrands 45), Carroll (Ameobi 45). Subs not used: Alnwick, Henderson.