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Dartford remain three points from safety in the Vanarama Conference after suffering a fourth straight league defeat on Tuesday night.
They conceded a goal at the end of each half against an Eastleigh side who are now just three points off the play-offs.
Darts had two good early chances at the Silverlake Stadium.
Max Cornhill’s free header from a Ryan Hayes cross was saved by Ross Flitney and when Dean Beckwith lost possession for the home side, Peter Sweeney ran clear but couldn’t convert his one-on-one with Flitney.
After that, it was all Eastleigh.
Jason Brown pulled off good saves to thwart James Constable and Ben Strevens before Stuart Fleetwood volleyed over from a good position. Beckwith delivered a great cross which Strevens should have scored from and Constable then hit the post from 12 yards out.
It looked like Dartford would reach the break on level terms but they fell behind in stoppage-time. They failed to pick up Midson from a Jai Reason corner and the former AFC Wimbledon man planted his header into the net.
Eastleigh went in search of a second goal after the restart. Midson had already gone close after a run and cross by Fleetwood before he forced an outstanding save from Brown.
Good link-up play between Constable and Strevens set up Midson for an effort which only missed by inches and Brown then held a Jamie Collins header from Reason’s cross.
Four minutes from time, the game was finally put beyond Dartford in bizarre fashion.
Michael Green’s low corner drifted all the way into the net to leave Tony Burman’s men deep in relegation trouble.