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Welling dropped two vital points in the chase of a Blue Square South play-off place on Saturday.
A stoppage time penalty denied the Wings victory over lowly Dorchester after a needless challenge by on-loan Charlton defender Carl Jenkinson.
The teenager, being watched by Addicks coach Mark Kinsella in the crowd, dived in when the ball was never there to be won to concede the spot-kick which Matt Groves drilled home.
It was a shattering blow for the Wings, who were in control throughout but their failure to add a second goal eventually proved their downfall on a day when victory would have closed the gap on the top five to just four points.
Andy Pugh (pictured) hit the post in the 16th minute before he won a penalty 60 seconds later after Gary Bowles brought him down.
Lee Clarke confidently tucked away the spot-kick but chances thereafter were limited as Welling failed to show the same fluency as on recent away trips.
Dorchester's Nathan Walker hit the bar from a corner and it was only from set pieces that Dorchester threatened Charlie Mitten's goal.
Pugh, denied by keeper Regan Coward just before the break, turned and hit the post six minutes into the second half.
Referee A Neil failed to protect the Welling players - particularly Sam Hurrell - as they were subjected to a number of late and rash challenges. Eventually he started to book the offenders but a stronger referee may well have started to reach for his red card.
Pugh's right-foot shot was beaten away late on as Welling looked to be heading for maximum points.
However, Dorchester, who failed to produce a serious shot on target throughout the 90 minutes got themselves a fortunate point when Jenkinson gifted them the spot-kick.
Welling could have regained the lead late on but Tom Whitnell and Pugh both had their efforts blocked before Clarke blazed over.
Welling host Weymouth on Tuesday night at Park View Road, kick-off 7.45pm.
Bromley went down 2-0 to Staines in the Blue Square South at Hayes Lane.
Ex-Bromley player Ali Chaaban gave the visitors a 19 minute lead before Marc Charles-Smith added a second after 76 minutes.
A George Porter double plus goals from Tommy Tyne and Ross Lover gave Cray Wanderers a 4-2 victory at Boreham Wood in the Ryman League Premier Division.