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Sam Corne produced a man-of-the-match display to lead Welling to the first home win since December on Saturday.
The teenager capped an impressive afternoon by scoring the third goal and moving Welling to within three points of safety.
The Wings now trail Alfreton by just three points but have the chance to go above them before the two sides meet in a relegation showdown next Saturday if Welling can beat Wrexham on Tuesday night.
Kidderminster arrived on the back of three directors, including their chairman, resigning the previous day and once behind they rarely threatened to get back into the game.
There were a couple of shaky moments for the Welling defence early on but once skipper Jake Gallagher headed in Kieron St.Aimie's pin-point cross, there was only going to be one winner.
Welling made it 2-0 on 35 minutes when St.Aimie chased down Ross Lafayette's header on. Keeper Danny Lewis came out to clear but fired the ball straight against the Wings striker and it rolled into the empty net.
Great skills by Dominic Vose nearly created a third goal as from his first pullback, St.Aimie and Gallagher went close and then second time around, St.Aimie somehow deflected the ball onto the underside of the bar from close range.
Welling deservedly went 3-0 ahead on 71 minutes. Corne, who won every header and covered so much ground at the heart of the midfield collected St.Aimie's flick and set a low left-foot shot beyond Lewis, who got a hand to it but couldn't deny the 18-year-old his first Wings goal.
Keeper Jon Henly beat away substitute Kevin Nicholson's late free-kick while veteran striker Lee Hughes was fortunate not to collect a second caution late on as the Wings eased to through to the final whistle.
Welling wore a pink kit to mark Ladies Day at Park View Road as the club raise over £3,500 for Jo's Cervical Cancer Trust.
Welling: Henly, Gallagher (Fagan 81mins), Vose, St.Aimie, Lafayette (Akinde 81mins), Jefford, Harris, Corne, Williams, Osborne, Chambers. Subs not used: Young, Berry, McEntegart. Attendance: 505.