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Welling lost their unbeaten home record in Blue Square Bet South to Eastleigh on Saturday.
Danny Smith’s 39th-minute goal proved decisive in a game devoid of much quality as both sides had nothing to play for.
Welling rotated their squad yet again but had enough chances to wrap the game up early on.
Loick Pires’ long-range attempt was tipped over and when Harry Baker returned the resulting corner, Scott Kinch somehow headed wide from a yard when it seemed easier to score.
Skipper Jack Parkinson was then guilty of another similar miss, volleying wide at the back post from a Baker free-kick.
Eastleigh, who struggled to string two passes together in the first half-hour, scored with virtually their first attack. Mitchell Nelson produced a cross of quality and Smith arrived to score beyond keeper Craig Holloway.
Substitute Lee Peacock wasted two good openings to double the lead as Eastleigh improved after the break.
Pires’ excellent drive went inches wide on the hour but, that apart, Welling struggled to put any consistent play together and it was not until the last minute that Pires (pictured) went close again, although his free-kick was comfortably saved.
With Sutton losing, the Wings are now all but assured of third spot, giving them home advantage in the second leg of the play-offs, with Sutton still their likely opponents.