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Joe Healy's first-half header ensured Welling made it back to back wins in the Skrill Premier on Saturday.
Following on from their 5-2 defeat of Forest Green, the Wings moved up to 11th after Healy (pictured) nodded in Jake Gallagher's 37th-minute cross.
After surviving a few early scares, it was a relatively comfortable win for Welling, although they failed to reach the heights of their previous outing.
Skipper Lee Clarke saw his 10th-minute header turned onto the post by keeper Nick Liversedge.
Healy then beat the offside trap on 34 minutes but failed to pick out one of four team-mates in the box.
It did not prove costly, however, as three minutes later, Gallagher spotted Healy's perfectly timed run and he directed his header beyond Liversedge.
Clarke had a goal ruled out for offside two minutes later as Ross Lafayette was stood on the goalline as the ball went in before the returning Blaine Hudson headed wide and Kurtis Guthrie failed to make the most of a great opening in stoppage time.
After the break, Hyde failed to trouble Welling keeper Lee Butcher until the final five minutes.
By then, Lafayette had wasted a good one-on-one chance and substitutes Loick Pires and Kiernan Hughes-Mason were both denied.
Butcher needed to be at his best in the 87th minute when he tipped over Scott Spencer's header after a long Will Haining throw-in was flicked on.
Welling entertain Aldershot on Tuesday night at Park View Road.