The Cards boss, who had to endure chants of 'Cockerill Out' 48 hours earlier, made four changes to the side that were thumped at Grays and started with two players in attack for the first time this season.
With a more attack-minded outlook, the effect was devastating as the home team, sparked by Goma Lambu, Guiseppe Sole and Stevenage's on-loan striker Jon Nurse, sent the home crowd away celebrating a three-point haul for the first time this campaign.
Goals from Craig McAllister, Sole and substitute Steve Ferguson were a welcome sight for Cockerill.
The hosts had a glorious chance to take the lead in the early exchanges when Karl Murray's floated centre from deep was met by centre-half Tom Hutchinson, but he thumped his free header over the bar from six yards.
Harriers certainly had the physical attributes needed at this level and striker Andrew White's presence, alongside former Premiership frontman Dean Sturridge, meant the visitors carried a threat in attack.
But it was Woking that snatched the lead, albeit in fortuitous fashion, after 27 minutes. Stuart Whitehead attempted to head a Nurse cross clear, but it rebounded off Steve Evans before ricocheting off McAllister and into Scott Bevan's net.
Five minutes later Lambu dispossessed Gavin Cowan and set up Sole, who fired home from the edge of the area to make it 2-0.
It was enterprising stuff from the Cardinals and they might have added another when Evans headed wide from Lambu's cross, before Bevan saved smartly from his left from Nurse.
Kidderminster defender Mark Creighton looked to have snatched a goal back before the break only for his header to be kept out by a combination of Evans and the crossbar.
Harriers boss Mark Yates threw on three substitutes in the early stages of the second half, but they failed to make an impact and the hosts went further ahead in the 77th minute.
An excellent header from McAllister set substitute Ferguson away and his left-foot shot flew in off Whitehead for the third.