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Welling made it four league wins in a row against mid-table Chippenham on Saturday.
Tom Bradbrook scored twice with Joe Healy and substitute Bradley Goldberg also finding the target.
They may have suffered an early FA Cup exit but Jamie Coyle's side are moving up the gears as far as their league form is concerned - they have now lost just once in their last 11 games.
Welling were without on-loan Colchester keeper Dillon Barnes due to his red card against Havant so Kleton Perntreou was between the sticks.
Perntreou, 22, was released by Palace at the end of the last transfer window. However the trio of Jamie Coyle, Jack Parkinson and Jack Jebb were all available to play - after their one-game suspensions cleared in Thursday night's London Senior Cup defeat to Corinthian Casuals.
Referee Lee Brennan took centre stage early on and was in danger of losing control at one stage.
He penalised Healy for an early challenge and promptly produced a yellow card for the next foul the Wings man made.
Chippenham's Dean Evans and Welling's Olumide Durojaiye followed into the referee's notepad - all inside the first 19 minutes.
Welling started to impresss as the half went on, Healy's header forced keeper Jared Thompson into action before boss Coyle headed over from close range when it seemed easier to score.
The breakthrough arrived seven minutes before the break as Jeffrey Monakana ran at the visiting defence before delivering an inch-perfect cross for Healy to head in from close range.
It was 2-0 on 42 minutes as Jebb's free-kick was headed in at the far post by Bradbrook.
Welling made the points safe just three minutes into the second half when Bradbrook headed in another Jebb cross.
Chippenham substitute Josh Smile was lucky to escape with a yellow card for an awful challenge on Ben Jefford.
The visitors could only test Perntreou from distance but the Wings keeper showed good hands on his debut.
Jebb was denied a deserved goal when his late free-kick was turned behind for a corner but Welling did add a fourth on 83 minutes.
A move from right to left ended with Jefford delivering into the danger area and substitute Goldberg slotting home from close range.
Goldberg nearly added another moments later but Jared Thompson made a smart save as Welling turned on the style in the closing stages.
Welling: Perntreou, Dymond, Jefford, Durojaiye, Coyle (Gayle 81mins), Parkinson, Monakana, Healy, Bradbrook (Phipps 70mins), Jebb, Nanetti (Goldberg 76mins). Subs not used: Sinclair, Pattisson.
Chippenham: Thompson, Bowman, Jones (Donnelly 63mins), Tindle, Richards, Ferguson, Smith (Felix 75mins), Pratt, Guthrie, Evans (Smile 46mins), Twine. Subs not used: Beeden, Horgan.
Attendance: 595.