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Welling's late fightback went unrewarded against National League South leaders Wealdstone on Saturday.
The Wings trailed 2-0 with five minutes to go but Adam Coombes converted a late penalty to give them hope.
They then missed a glorious chance to snatch a point in the second minute of stoppage time, but substitute Aaron Cosgrave was denied when sent clean through on goal.
Welling had started brightly although former Wings forward Ross Lafayette blazed over a glorious chance for the visitors inside six minutes.
The hosts had gone close moments earlier but keeper Aston Oxborough - on loan from Premier Division Norwich - did well to turn away Coombes' header from an Anthony Cook free-kick.
Bradley Goldberg and Cook both went close as Welling continued to create chances in a bright start to the game.
Wealdstone were not without their openings, though, Daniel Green going close after Rob Swaine's misplaced header.
On-loan midfielder Theo Widdrington nearly marked his Welling debut with a goal, but his 20-yard right-foot shot came back off the post just past the hour.
Nonetheless it was an impressive display from the midfielder, who gave a more measured look to the heart of the Wings midfield and looked comfortable with everything he did.
Sparked by the scare, Wealdstone's response was swift with two goals inside nine minutes as they wrestled control of the contest.
A corner needlessly given away by Jay Rich-Baghuelou, filling in again in the unfamiliar right-back role, was turned in at the far post by the unmarked Michael Phillips on 69 minutes.
Then, runners down the left were not tracked and Wealdstone took full advantage, Dennon Lewis finishing off an incisive move by slotting home an excellent second goal.
Welling were given a lifeline five minutes from time when Coombes' shirt was tugged in the box. It was a simple decision for referee Rob Whitton - who was fussy throughout - to give. Coombes fired in the spot-kick via the underside of the bar.
Substitute Nathan Green headed just wide from a corner and then Cosgrave burst clear - after Coombes somehow kept the ball in - only for Oxborough to block his effort when the striker could have gone round him instead.
Welling: Wilks, Rich-Baghuelou, Anderson, Widdrington (Jebb 81mins), Swaine, Okosieme, Cook, Agyemang, Goldberg (Cosgrave 72mins), Coombes, McCallum (Green 60mins). Subs not used: Rooney, Oyinsan.
Wealdstone: Oxborough, Arnold, Efete, Clifford (Sheppard 81mins), Stevens, Okimo, Phillips, Mendy (Smith 60mins), Lafayette, Green, Lewis. Subs not used: Roberts, North, Watt.
Attendance: 594.