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Spirited Welling showed plenty of fight against Halifax on Saturday but were undone by a second-half penalty.
The game was ultimately decided by Lee Gregory's 50th-minute spot-kick, awarded for a professional foul that saw Blaine Hudson sent-off for the second time this season.
Despite having 10 men, Welling gave as good as they got in the second half but never got a break in front of goal.
Welling should have been ahead inside the opening 35 seconds but on-loan Charlton forward Tobi Sho-Silva, having forced an error from the Halifax defence, directed his header over keeper Matt Glennon but also over the crossbar.
The hosts, already stretched defensively with illness ruling out Tom Bender, lost Connor McLaren to a knee injury in the opening 15 minutes.
Toby Ajala's low shot was saved before skipper Lee Clarke, back in the starting line-up with Jake Gallagher suspended, failed to connect properly from Joe Healy's set-up.
Hudon was caught out on 34 minutes and the dangerous Gregory turned makeshift right-back Josh Wakefield in the box but dragged his shot wide of the near post.
The game turned early in the second half when another Halifax long ball caught out the home defence and, having bundled his way past keeper Jamie Turner, Gregory went down under the challenge of Hudson.
Referee Dean Treleaven was left with no choice but to point to the spot and show the red card, Gregory sending Turner the wrong way to put his team ahead.
Welling's response was immediate. Harry Beautyman's right-foot shot forced Glennon into a one-handed save and Healy's follow-up was deflected wide for a corner when it could have easily bounced in.
Wakefield's free-kick had Glennon scrambling again and while Halifax had the greater possession, they never had a cutting edge to put the game out of reach, with Welling coming up just short in the closing stages as they aimed for an equaliser.