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Goals in either half from Reece Harris and Ricky Wellard earned Welling a second successive win in the National League on Tuesday night.
Welling boss Loui Fazakerley will be delighted with the industrious display that saw his side move up to 18th in the table.
Both teams had chances in an open first half when neither side remained in control for long as the game went from end to end.
Wellard twice went close for Welling while Chester threatened through John Rooney.
The visitors should have gone ahead on 22 minutes but Craig Hobson failed to connect properly with a right-wing cross and the ball fell safely to Wings keeper Tom King.
Welling had a goal disallowed for offside when Ben Jefford turned in a header back across goal just past the half-hour.
Chester went close again moments later when another right-wing cross was met by Ross Hannah this time and the former Grimsby man saw his volley come back off the post.
That lack of quality in front of goal was turned around two minutes before half-time with a stunning goal for Welling.
The hard-working George Porter won the ball back inside his own half to start the move. Harris collected Xavier Vidal's crossfield pass and his touch appeared to take him too wide, until he produced a delicious left-foot chip over keeper Jon Worsnop.
Ironically, Harris' only previous Welling goal was also against Chester, last season in a 3-1 home defeat.
After the break, Wellard again threatened, playing in his preferred role just behind the lone striker.
The hosts had more of the ball, limited Chester to half-chances and were showing signs of the battling spirit that saw Fazakerley keep them up against the odds at the end of last season.
It was no surprise, therefore, that Wellard added Welling's second goal with 20 minutes left. A left-wing corner was nodded towards goal by Jefford and when Worsnop fumbled what appeared to be a regulation save, Wellard was on hand to bundle the ball home.
It was no more than Welling deserved as they dominated the second half, both in terms of possession and chances.
Nortei Nortey impressed at right-back while the defensive pair of Michael Chambers and Kevin Lokko held firm.
Chester substitute Kane Richards was booked for a dive five minutes from time when a penalty looked certain to be given after Lokko's challenge while Hannah hit the post for the visitors again in the 90th minute as Welling's goal led a charmed life.
Their defence was finally beaten in the fourth and final minute of stoppage time when Hannah turned the ball in at the near post. But referee Robert Whitton blew shortly after the restart and Welling moved up to 18th place ahead of Saturday's home game with FC Halifax.
Welling: King, Jefford, Chambers, Porter, Lee, Wellard, Nortey, Lokko, Corne, Harris, Vidal (Kabba 82mins). Subs not used: McEntegart, Obafemi, Taylor, Awotwi.
Chester: Worsnop, Higgins, Hunt, Sharps, Shaw, Hannah, Rooney (Hughes 72mins), Chapell, Thomson (Mahon 67mins), Hobson (Richards 67mins), Heneghan. Subs: Forth, Kay.
Attendance: 564.