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Two second-half goals from Vasilious Karagiannis and Ross Lafayette handed Welling their first win in six Skrill Premier games on Saturday.
And the Wings celebrated the news that boss Jamie Day has agreed a new two-year deal to stay in charge at Park View Road - despite having midfielder Jake Gallagher sent-off on the half-hour.
Gallagher saw red after a late and needless challenge on Chester's Jason Jarrett. Referee Daniel Cook was in close attendance and wasted little time deservedly getting out the red card.
Welling should have already been ahead by that stage with skipper Lee Clarke failing to get a true connection from close range and being denied by keeper Aaron Chapman, who then saved the rebound.
With Welling down to 10 men, Chester nearly went ahead when Craig Mahon's deflected right-foot shot went just over the bar.
But Welling, who had picked up a second red card in three home games, were giving as good as they got, with Lafayette twice going close before the break.
In the second half, Welling again belied their numerical disadvantage. They went ahead on 57 minutes as Tobi Sho-Silva set Karagiannis clear and he delivered an excellent low left-foot shot beyond Chapman.
Lifting his shirt above his head to celebrate, Karagiannis was promptly booked and then, before the game restarted, he was replaced by Toby Ajala as boss Day made a planned substitution regardless of the goal.
The work-rate of Clarke and Harry Beautyman in the middle of midfield, after Gallagher's red card, was underlined by a double substitution with 25 minutes left, as Day introduced Joe Healy and Josh Wakefield in their positions.
Chester enjoyed plenty of the ball but it was never in a position to hurt Welling, who kept two banks or four and broke with pace and purpose.
With five minutes left, Healy fed Sho-Silva but his right-foot effort went wide when it seemed easier to finish with his left foot.
But it mattered little as in the 89th minute Wakefield danced his way past two defenders and picked out the unmarked Lafayette, whose right-foot volley went in off the far post for his 13th goal of the campaign.
Welling's win lifted them up to 13th and they did neighbours Dartford a favour, as they closed the gap to Chester to three points after they won 2-1 at home to Macclesfield.