
Walker's first-half strike was the only goal of the night, but in truth the margin could have been far more emphatic, however the Seasiders found a way to win on the back of a disappointing 2-0 away defeat at Gainsborough Trinity the previous Saturday.
Whitby, who had made several changes from that reverse in Lincolnshire, dominated from the first whistle, with Aaron Braithwaite striking an opportunistic effort towards goal in the first four minutes.
Walker then should have given the Blues the lead ten minutes later when he was picked out by Jacob Gratton. Walker went for goal but could only strike the woodwork from close range.
Just a minute later, as Whitby continued to take the game to their Derbyshire opponents, Walker was involved once more, this time being denied by a close range save from Saul Deeney.
In the 29th minute, a rash defensive challenge presented Whitby with another opportunity to get their noses in front but Gratton's 25-yard free-kick flew narrowly off target.
But the hosts wouldn't be denied seven minutes later when Lewis Hawkins played the ball into Walker, who left a defender sliding helplessly and Deeney diving in the opposite direction, before calmly slotting the ball home into an empty net.
In the second half, Walker sent a low strike wide of the post as Whitby looked to double their advantage, then Aaron Haswell went for goal, only for his left-footed effort to drift wide of the opposite upright.
At the other end, Kornell McDonald gave Town a slight scare as he volleyed wide of the mark but Shane Bland always looked confident that the strike wouldn't threaten him.
The Seasiders continued to push in the final stages with Junior Mondal curling an effort into the hands of Deeney in what was the last real opportunity of note.
But then in stoppage time, a moment of madness from Matlock goalkeeper Deeney saw him sent off after picking the ball up outside his area. Centre-back, Ioan Evans, would have a brief spell between the sticks for the Gladiators, but he wouldn't be tested as Whitby opted to protect their one-goal advantage.