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Ebbsfleet were denied victory at Staines on Saturday by an own goal in stoppage-time.
Michael Corcoran headed the ball past Fleet keeper Preston Edwards just as the Fleet looked set to inflict only the Swans' third home defeat of the season.
A first-half goal from Ben May had given them the lead, the centre-forward vindicating manager Steve Brown's decision to restore him to the starting XI at the expense of Michael Thalassitis.
Staines came into the game as the form side in Skrill South, having won five of their previous six games.
But they looked out of ideas until Corcoran's late moment of misfortune.
Ebbsfleet made the early running on a near-perfect pitch at Wheatsheaf Park. Right-back Joe Howe was their best attacking outlet and one of his crosses dropped tantalisingly between Billy Bricknell and Anthony Cook.
Howe was then in the thick of the action at the other end, making a brilliant last-ditch tackle to dispossess Stephane Ngamvoulou as he burst into the Fleet box.
Staines took a while to get going and when they did, they barely troubled goalkeeper Edwards, who easily saved Ngamvoulou's cross-shot.
But just as the Swans were starting to impose themselves, they fell behind. May controlled a ball in from the right and lifted it over his marker's head before prodding it into the net with his left foot.
Tempers started to fray as half-time approached. Staines right-back Sanchez Ming had already been involved in one tussle with May when he was booked for tripping Daryl McMahon.
Ebbsfleet continued to pose the greater attacking threat. Corcoran played a slide-rule pass into May's feet and Bricknell then worked a yard of space in the box, but he couldn't get his shot away.
Jerson Dos Santos cut in from the Staines left at the other end but he dragged his shot well wide.
The home side brought on former Fleet striker Calum Willock for the start of the second half but it was Brown's side who registered the first effort after the restart, Bricknell firing a half-volley off-target.
Willock's introduction meant the home side were now playing three up front, although their play was still lacking any real dynamism. And the Fleet, now operating on the counter-attack, looked the more likely scorers.
Bricknell was marginally offside when McMahon's through-ball sent him clear and Turner did well to gather a swirling Cook cross.
Ebbsfleet's two centre-backs then combined to lay on a good chance for Bricknell when Staines failed to clear a corner. Osei Sankofa's whipped cross from the left was turned goalwards by Anthony Acheampong and Bricknell scooped the ball over from close-range.
Just as the game seemed to be drifting, it came to life again.
Staines substitute Bajram Pashaj went on a storming run and Edwards did well to claw his shot out of the bottom corner. That was followed less than a minute later by a good chance for Thalassitis, who'd come on for May, although the on-loan Stevenage man dragged his shot wide.
The job looked to be done for Ebbsfleet but then came a moment Corcoran will want to forget. Max Worsfold drilled in a cross from the left and Corcoran, trying to clear, only succeeded in heading the ball past the stranded Edwards.
Staines: Turner, Ming, Worsfold, Ferrell, M'Boungou, Ifil, Lodge, Ngamvoulou (Brown 59mins), Theophanous, Dos Santos (Pashaj 59mins), Beadle (Willock 46mins). Subs not used: Merson, Neville.
Ebbsfleet: Edwards, Howe, Acheampong, Sankofa, Palmer, Corcoran, McMahon, Rance, Cook, May (Thalassitis 74mins), Bricknell (Osborn 90mins). Subs not used: Sessegnon, Hall, Huke.
Attendance: 362.