Harriers started the second half on the attack with Henriksen flashing a 20-yard drive wide of Rogers' left-hand post on 48 minutes.
The first booking arrived four minutes later with Parrish cautioned for a foul on Morrell.
Then Wrexham's Paul Edwards followed on 58 minutes for a challenge on Melligan.
Harriers burst forward on the hour and Bishop played a right-wing cross into Henriksen who hooked the ball marginally over the bar while under pressure.
A minute later Wrexham had a good chance when Whitley shot deflected into the path of Jones but he turned to fire wide from 12 yards.
Wrexham, already a goal down, were hit further on 63 minutes with a red card for midfield general Ferguson after stamping on Melligan.
But within two minutes the home side could have drawn level when Morrell found himself goal side of Ayres but the top scorer's low drive was well turned away by the agile Brock low to his right.
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