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A wonder goal from Matthew Paterson was the highlight as Welling maintained their remarkable weekend record on Saturday.
Welling are yet to taste defeat on a Saturday in the league this season as they kept pace with the leading lights in National League South.
All three of their defeats have come on Tuesday nights and they were never in serious danger of slipping up against bottom side Weston.
As always, Weston had plenty of possession but they failed to really hurt the hosts with the ball.
Welling started brightly and centre-back Yannis Ambroisine volleyed against the crossbar inside the third minute before Nassim L'Ghoul's follow-up was beaten away by keeper Luke Purnell.
The Wings did go ahead on six minutes, however, as a clever flick by Brendan Kiernan set up skipper David Ijaha, who found the top corner with a crisp 25-yard strike.
Weston equalised in the 19th minute after a goalkeeping howler by Dan Wilks. The Welling keeper came rushing out of his box to clear but the ball fell perfectly for Tom Llewellyn to brilliantly lob home into an empty net from 40 yards.
Paterson then produced a magical moment to put Welling ahead two minutes later. Collecting a long ball forward, Paterson flicked the ball over his marker before an audacious chip over Purnell from the edge of the area went in via the far post.
Paterson had two openings to add to his tally either side of the break but failed to take advantage.
Referee Rob Whitton's laidback approach rubbed off on the players as the game failed to get out of first gear for long periods of the second half.
Weston should have levelled six minutes from time with their only noteworthy attempt at goal in the second half but Gethyn Hill blazed over after a free-kick was only half-cleared.
Welling wrapped the points up with a breakaway third goal in the fifth minute of stoppage time, Montel Agyemang playing in L'Ghoul, who rounded the keeper before slotting home.
Welling: Wilks, McNamara (Orlu 90mins), Genovesi, Ijaha, Ambroisine, Audel, Kiernan, Agyemang, Paterson (Goldberg 74mins), Mills, L'Ghoul. Subs not used: Marsh-Brown, Mendy, Kissock.
Weston: Purnell, McGrory, Nurse, Byrne, Pope, Bower, Hill, Lee, Jackson (Lucas 78mins), Myris Williams (Swallow 64mins), Llewellyn. Subs not used: Kingston, Morris Edwards, Thomas Barker.
Attendance: 622.