Steve Williams wasted another chance for the Shaymen when prodding wide from close range, but Halifax took the lead on 34 minutes through Maynard, who fired the ball into the bottom corner for his first of the season.
That advantage was doubled five minutes later when Peniket made the most of a defensive lapse from Kidderminster before driving the ball past goalkeeper Lewis from an acute angle.
Peniket nearly put the contest out of sight after the restart but after his close-range attempt was saved, Kidderminster began to enjoy a better spell on the ball, with Michael Gash sending a header over the crossbar from eight yards.
Kidderminster produced a remarkable recovery at Barnet last weekend, and the way that they pressurised the home defence during the middle stages of the second half suggested that they were capable of pulling off another shock.
Centre-back Cheyenne Dunkley nearly added his fifth of the campaign in the closing moments but after his header struck the post, Halifax saw out the final minutes to move into second place in the standings.