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Jamie Day's first game in charge of Ebbsfleet will be an FA Trophy first round replay away to his old club Welling on Tuesday night.
There was nothing to separate the sides at the PHB Stadium on Saturday, where ex-Wings defender Anthony Acheampong cancelled out Kieron St Aimie's penalty for the visitors.
Welling played for more than half the game with 10 men after Joe Taylor was shown a straight red card for a bad tackle on Dean Rance.
But the Fleet couldn't break down their Vanarama Conference opponents after the break in what was Daryl McMahon's final game as caretaker manager.
With regular left-back Joe Howe suspended, Shane Huke was drafted into the Ebbsfleet defence. McMahon chose to name himself on the bench, with Rance returning after a ban to play in midfield.
There were two changes to the last team which Day picked as Welling manager. On-loan Crystal Palace defender Michael Chambers missed out through injury and Ben Jefford dropped to the bench, with Chris Bush and teenager Taylor coming into the starting XI.
Welling made a strong start and had the better of the early chances.
Michael Corcoran lost possession in a dangerous area and he was almost punished by Aristide Bassele, who ran forward and dragged a shot across the face of goal.
When a cross from the left pin-balled around in the Fleet area, Tyrone Marsh might have broken the deadlock but his shot was well blocked.
Huke was then cautioned for a challenge on the corner of the box and the resulting free-kick was rolled by Joe Healy to Bush, whose low strike fizzed past the near post.
Then came the first opening for Ebbsfleet. Matt Godden helped the ball into Billy Bricknell's path and he forced a good save from Welling keeper Benji Buchel.
A good move from the home side then saw Chris Sessegnon set the ball for Matt Johnson, whose swirling cross from the right was headed over by Rance.
Buchel was in action again moments later, standing tall to deny Godden when he swivelled in a crowded penalty area.
But when Marsh's heels were clipped by Huke just inside the Fleet box, St Aimie kept his cool to score from the spot. His low strike flew into the bottom left-hand corner despite the best efforts of Brandon Hall, who dived the right way.
Welling looked comfortable at this point. They almost doubled their lead when Healy crossed from the left and Bassele, under pressure from Huke, turned the ball wide.
Things were about to change, however. Taylor dived in on Rance and the Fleet midfielder reacted angrily. Referee Justin Amey wasn't impressed, either, brandishing a red card.
Worse was to follow for the visitors. Cook whipped over the free-kick from the spot where the red mist had descended for Taylor and one of the men in red - Acheampong - pounced to score from a yard out when the ball ran loose at the back post.
McMahon came off the bench just before the hour and he was straight into the action with a swerving shot from 25 yards which Buchel did well to gather.
It looked like the visitors were about to be reduced to nine men when Bush caught Cook in the face with an flailing arm. But Mr Amey chose to show only yellow on this occasion and no-one in red could get the vital touch to McMahon's fizzing free-kick from the right-hand touchline.
Welling couldn't get out of their own half and Godden arrowed a shot across Buchel which flew just wide.
On and on drove the Fleet. Godden crossed from the right and Cook was co close to making it 2-1 with a stooping header back across Buchel. The ball dropped inches wide.
Acheampong should have glanced in Cook's free-kick from the left but failed to make contact.
However, when the Wings did break their shackles, they should have snatched a late winner. Sam Corne's clipped pass sent St Aimie running clear but just as he was about to pull the trigger, Kenny Clark came from nowhere to thwart him with a brilliant last-ditch tackle.
Ebbsfleet: Hall, Sessegnon, Acheampong, Clark, Huke (Pooley 39mins), M Johnson (McMahon 56mins), Rance, Corcoran (Kiernan 76mins), Cook, Godden, Bricknell. Subs not used: Hughes, Shields.
Welling: Buchel, Taylor, Fyfield, Bush, Williams, Healy, Corne, Fagan, Bassele (Hudson 88mins), St Aimie, Marsh. Subs not used: Henly, A Johnson, Jefford.
Attendance: 876.