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Welling moved up to a season-best position of sixth in The Skrill Premier on Saturday after seeing off Tamworth.
Second-half goals from captain Lee Clarke and Loick Pires proved enough for the Wings, who have now lost just once in their last eight league games.
Clarke went close with two headers from corners before Pires, leading the line in the absence of the injured Ross Lafayette, broke the offside trap but dragged his left-foot shot wide of the far post.
The lively Lateef Elford-Alliyu then fired a shot against the crossbar on 24 minutes from outside the penalty area before Welling also hit the woodwork. Alex Dyer’s deep corner was met by the on-loan Baily Cargill, whose header hit the crossbar.
Wings keeper Lee Butcher turned behind Lloyd Kerry’s low drive as the chances continued to come at both ends, Pires’ flick set up Welling’s Joe Healy just before the break but keeper Cameron Belford diverted his shot for a corner.
Both sides went close at the start of the second half, Pires denied by Belford and Butcher keeping out Elford-Alliyu.
Tamworth lost former Gills defender Jack Evans to injury on 54 minutes after a crunching challenge by Jake Gallagher, who was cautioned for his troubles.
Welling finally broke the deadlock after 63 minutes. Kurtis Guthrie headed on a long free-kick and Clarke nodded in from 10 yards beyond Belford.
Richard Peniket missed a glorious opening to level moments later before Wings substitute Kiernan Hughes-Mason sent Pires clear but he cut back inside and the chance was gone.
Welling made the game safe seven minutes from time when the impressive Gargill exchanged passes down the left wing and delivered a perfect cross for Pires to slot home a goal that he deserved for his efforts.
The Wings travel to FC Halifax Town next Saturday.