The young striker helped Luton to the final of last season's competition while on loan and scored as they beat Scunthorpe 3-2 at Wembley. He was on target again with a well-taken 30th-minute goal which settled a well-contested game between two equally good sides.
Brentford twice went close to gifting the Canaries the lead in the opening 10 minutes with a poor back pass letting in Martin and a miss-kick from goalkeeper Lewis Price offering Tom Adeyemi a sight of an unguarded goal.
Fortunately for the visitors neither chance was taken, although it needed a goal-line clearance from Karleigh Osborne to deny Adeyemi from all of 40 yards.
But the Canaries did take the lead on the half-hour mark with a well worked goal. A quick break for Goran Maric found Martin on the edge of the box and the youngster did the rest, finding the back of the net from some 20 yards out via an upright.
Brentford had plenty of possession after the break but could not find an equaliser, with Marcus Bean's 57th-minute header from a corner, which was superbly saved by Ben Alnwick, the closest they came.