Boro are now 15th in National North with their faint play-off hopes looking all but over.
The Seadogs were again hit by illness and injury with Cam Wilson and skipper Will Thornton both missing.
Jono Greening's men then fell behind to Alfreton inside two minutes at Scarborough Sports Village.
They conceded again early in the second half and that's how it stayed.
Boro missed a host of chances with Michael Woods and Harry Green coming close early on.
McKenzie and Green then fired over the top late on.
Greening spoke to SAFC TV after the game:
Boro are back in action, in National North, on Saturday.
The Seadogs go to Scunthorpe United, next weekend.


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