Harriers finally posted their first shot on target on 70 minutes but Ayres' hanging header from a Parrish corner was easily held by Bastock in the Boston goal.
Within a minute Harriers were forced to play with 10 men as Bennett limped off with a hamstring strain after they had made all three substitutions.
Frustrated forward Henriksen was booked on 73 minutes for persistent misconduct. Bo Henriksen
Boston made their second substitution on 76 minutes with a straight swap upfront as Douglas was brought on for Duffield.
Harriers nearly forced their way onto the score sheet on 77 minutes with Bastock making an excellent tip over to deny Parrish's fierce half-volley from the edge of the area.
A minute later Henriksen fired wide at the near post for the visitors but their performance still struggled to reach any great heights.
They conceeded a third goal on 83 minutes to Logan who shrugged off Ayres and calmy beat Digby.
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