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Xavier Vidal scored all four goals as Welling reached the first round of the FA Cup for only the second time in 10 years on Tuesday night.
The scoreline certainly flattered Welling who looked edgy for the opening hour against the Ryman League Premier Division visitors.
Grays had the better of the first game on Sunday, which ended 1-1, but they were made to pay in the fourth qualifying round replay for missing a second-half penalty.
Welling took a 22nd-minute lead when Vidal's right-foot shot was only parried by keeper Lamar Joseph-Johnson and the loose ball fell perfectly for him to slam home from close range.
The game hinged on a 50th-minute penalty. Joao Carlos was bundled over in the box but captain Sean Cronin opted for power from the spot and keeper Mike McEntegart saved with his right hand before the rebound was blocked by Ben Jefford.
Within six minutes, Welling were two-up. Substitute Michael Bakare, on in the first half for Sahr Kabba, worked his way down the left and crossed for Vidal to head in.
The game was settled as a contest on 62 minutes when Vidal produced a neat right-foot finish as Wings broke with pace.
Vidal then scored his fourth of the night on 76 minutes, an excellent right-foot finish into the far corner from 20 yards.
He became the first Welling player to score four goals in a game since Lee Clarke achieved the feat against Eastleigh.
Welling eventually progressed with some ease but they will need a much-improved performance when they travel to Barwell in the first round.
The 4-0 thrashing could have been even worse for Grays in injury time but Wings substitute Kurtis Cumberbatch shot narrowly wide.
Welling: McEntegart, Jefford (Obafemi 77mins), Fagan (Cumberbatch 81mins), Chambers, Kabba (Bakare 21mins), Wellard, Lokko, Corne, Harris, Williams, Vidal. Subs not used: Cotterill, Gunner, Johnson, Fitchett.
Attendance: 733.