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Welling conceded an injury-time penalty to lose to Bishop's Stortford in National League South on Tuesday night.
The Wings had led at half-time against the run of play and they were beaten four minutes into stoppages when Bradley Woods-Garness tucked home a spot-kick.
Stortford had the first attempt at goal on 13 minutes when Welling keeper Chris Lewington had to clear Dominic Green's 25-yard left-foot free-kick with his legs.
Welling soon changed their 4-5-1 formation to 4-4-2 as they lacked an attacking threat, although it was their failure to retain possession in forward areas that saw them concede the ball cheaply too often.
Stortford almost broke the deadlock just after the half-hour. Tambeson Eyong collected the ball deep inside his own half from the keeper and advanced down the left wing unchallenged. He cut into the penalty area but saw his right-foot curler come back off the upright and cleared to safety by the hosts.
Welling made Stortford pay a minute before the break. A succession of corners was finally rewarded when Sam Hatton's corner was headed in by Slabber.
The visitors should have been level three minutes into the second half but Eyong somehow headed a free-kick across the face of goal.
It was third time lucky for Eyong on 61 minutes when Welling gave the ball away on halfway and the Stortford midfielder drilled home before a strange, and needless, celebration in front of the home dugout.
Welling made three changes after the break but never created much as an attacking force, although they appeared to be heading for a draw until a late trip in the box handed Stortford a penalty in stoppage time.
Welling: Lewington, Nelson, Brown, Corne, Francis, Leacock, Whitely (Smith 55mins), Waldren, Slabber, Hatton (Joseph-Dubois 68mins), Sprague (Johnson 72mins). Subs not used: Banton, Hayles.
Attendance: 502.