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Hudson headed in Harry Beautyman's right-wing cross from close range just after the hour mark to reward the Wings for a patient display in front of goal.
Like Gateshead before them on Tuesday, Macclesfield struggled in the second half and it took them until the 75th minute to register their only effort at goal during the second 45 minutes.
Chances were few and far between in the first half although Tobi Sho-Silva was prominent early on and Ross Lafayette saw an early drive saved by keeper Rhys Taylor.
Hudson should have scored straight after the restart but, with space at the far post from a short corner, he somehow blazed over when it a goal seemed certain.
Alfie Mawson was denied his second goal in a week when his header was cleared to safety before Welling went ahead on 62 minutes as Toby Ajala set up Beautyman, whose cross was converted by Hudson.
Sho-Silva nearly got a deserved second goal four minutes later when his persistence took him past Andrew but keeper Taylor was out smartly to save.
Lafayette headed over, Sho-Silva was penalised for handball amid claims that he was fouled when racing clean through and then Lafayette shot weakly at Taylor.
Welling comfortably closed the game out as Macclesfield failed to put Turner under any serious pressure.
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