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Ebbsfleet dropped to fourth place in National League South after twice coming from behind to draw with play-off hopefuls Chippeham on Saturday.
With Dartford thrashing Slough, it meant they overtook the Fleet and sit third in the table with two games remaining.
Chippenham went close to a breakaway goal on 13 minutes when Chris Solly, moved into the midfield, gave the ball away and the visitors sent Jordan Bray clear. He cut inside on his left foot but his low shot came back off the post and was cleared to safety.
There was a significant mood change midway through the first half among the Fleet fans as the home side were penned back inside their half.
Fleet were trying to play out from the back but were frustrated by a Chippenham outfit who got their reward with a stunning opener on the half-hour.
Joe Hanks sent a spectacular right-foot shot into the far corner from 25 yards beyond the despairing Louie Moulden.
Despite their below-par show, the Fleet - and striker Elliott Romain - had enough chances to be level, if not ahead, by the break.
Romain saw his header from a Chris Solly corner cleared off the line by Landon Golding on 33 minutes. Then, from the resulting corner, Romain was denied not once, but twice, from close range.
Fleet keeper Moulden had to turn over Hanks’ header as Chippenham went close to a second.
Solly was booked on the stroke of half-time for a challenge on Alex Bray. The visitors wanted a red card for a two-footed tackle while Fleet claimed he won the ball. Referee Steven Hughes called it about right.
Fleet boss Dennis Kutrieb replaced Alex Finney with Craig Tanner at the break and it took just five minutes for the home side to level the scores.
Solly’s left-wing corner was met by the unmarked Romain who headed into an empty net with keeper Will Henry caught in no man’s land.
Shaq Coulthirst’s low shot was saved by the legs of Henry as the Fleet started to dominate, although that was his last involvement as the home side introduced leading scorer Dominic Poleon just before the hour mark.
But the tide shifted again on 61 minutes. Keeper Moulden appeared to have kept the ball in play but the assistant referee awarded a corner from the far side.
When the ball was played in, centre-back Will Richards powered his header beyond Moulden to give Chippenham the lead.
Hanks nearly wrapped the points up with 20 minutes left but his brilliant right-foot curler from 25 yards came back off the angle of post and bar.
Fleet’s Rakish Bingham and Romain were both denied as Chippenham defended stoutly but their resistance was broken 12 minutes from time when Solly volleyed in Tanner’s free-kick at the far post.
It was all Ebbsfleet. Substitute Lee Martin beat the offside trap but struck the post from 20 yards, and Poleon was unable to turn in Chapman’s cross.
Then Poleon opted against an early cross the unmarked Martin as Fleet pushed for a winner and in the fourth minute of stoppage time a brilliant stop by Henry denied Martin the winner.
Ebbsfleet: Moulden, J Martin, Jombati, N’Guessan, Bingham, Romain (L Martin 78mins), Solly, Paxman, Chapman, Finney (Tanner 46mins), Coulthirst (Poleon 59mins). Subs not used: Haigh, Domi.
Chippenham: Henry, Golding (Santos 68mins), Greenslade, Parselle, Richards, Dabre, Young, Bray, Hanks (Bradbury 79mins), Mehew, Russe. Subs not used: Coppin, King, Lawal.
Referee: Steven Hughes.
Attendance: 1,102.