Vines' position was under scrutiny before the game following a poor start to the season but it took three minutes for that to change when Harriers handed the home side the lead.
Daryl Burgess scored an own goal when he diverted the ball past keeper John Danby as he tried to clear the cross from Andy Lindegaard.
The visitors almost hit back just past the half-hour mark when Michael Blackwood was left all alone the area and had a snap-shot blocked at point-blank range by keeper Scott Ward.
Ward was making his first league start for Crawley and did well again on the stroke of half-time with a full-length save to stop Blackwood's 20-yard drive.
Blackwood was left frustrated again early in the second half when he curled a free-kick just wide of an upright.
Crawley went close on the hour mark when Lindegaard headed over from close range following good work by Daryl Clare, before they sealed the points late on.
Jamie Cade outpaced defender Mark Jackson eight minutes from time and fired through the legs of Danby for his first goal of the season.
Harriers were reduced to ten men a minute later when Terry Fleming was sent off for a second bookable offence.
Daryl Burgess scored an own goal when he diverted the ball past keeper John Danby as he tried to clear the cross from Andy Lindegaard.
The visitors almost hit back just past the half-hour mark when Michael Blackwood was left all alone the area and had a snap-shot blocked at point-blank range by keeper Scott Ward.
Ward was making his first league start for Crawley and did well again on the stroke of half-time with a full-length save to stop Blackwood's 20-yard drive.
Blackwood was left frustrated again early in the second half when he curled a free-kick just wide of an upright.
Crawley went close on the hour mark when Lindegaard headed over from close range following good work by Daryl Clare, before they sealed the points late on.
Jamie Cade outpaced defender Mark Jackson eight minutes from time and fired through the legs of Danby for his first goal of the season.
Harriers were reduced to ten men a minute later when Terry Fleming was sent off for a second bookable offence.