Martin was denied by an excellent save from Tim Krul in the 13th minute but made no mistake when he was presented with one of the easiest goals he will 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 they did 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.
Newcastle were thwarted in their quest for an equaliser in the 89th minute when Peter Lovenkrands headed Shane Ferguson's cross against the crossbar.