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Ebbsfleet are still in the FA Trophy after holding Conference side Braintree to a draw at Cressing Road on Tuesday night.
Adam Cunnington marked his full Fleet debut with an early goal but Iron skipper Kenny Davis scored from the penalty spot to restore parity on the stroke of half-time.
Ebbsfleet had the best of the second-half chances but these two sides must reconvene at the PHB Stadium in a week's time for the right to visit North Ferriby in the quarter-finals.
Both teams were playing for the first time in 10 days, this third-round tie having been postponed on Saturday because of a waterlogged pitch.
Braintree made just one change from their previous outing, Dan Sparkes replacing the injured James Mulley.
For the visitors, who were coming off the back of a 2-1 defeat at Sutton, there were two enforced changes. Daryl McMahon has since left Fleet to sign for Boreham Wood, while Tyrone Marsh is cup-tied in this competition.
McMahon's place in central midfield was taken by Matt Johnson, while there was a recall after suspension for defender Anthony Acheampong. He lined up alongside Kelvin Langmead and Kenny Clark in a back-three as manager Jamie Day - who named himself on the bench - switched formation.
The home side had the first chance when Jordan Cox got his head to a deep cross from the left. But his effort stopped in the mud and Preston Edwards was able to gather.
Ebbsfleet took the lead in the fourth minute.
Joe Howe won a corner down the left-hand side and Stuart Lewis' flat delivery was bundled in at the near post by Cunnington despite the best efforts of his marker.
At the other end, Edwards held a Cox header and then watched a Simeon Akinola effort deflect wide of his far post after the forward had turned inside Acheampong.
Then came a Fleet move which probably deserved a goal. Stuart Lewis played a neat ball into the path of the overlapping Johnson and his cutback was met on the volley by Theo Lewis. The ball was heading inside the near post when goalkeeper Nick Hamann dived to his left to palm it behind.
Howe's evening ended prematurely when he tangled with Chez Isaac inside the Fleet box, landed awkwardly and walked off holding what looked like a dislocated shoulder.
Davis fired a long-range effort over the bar for Braintree before the visitors carved out another fine chance.
Cunnington got up well in the box to nod down Matt Fish's high cross for Johnson. The midfielder got his toe to the ball before Hamann but watched as his effort bounced agonisingly wide.
Ebbsfleet survived a nervous moment when Langmead sliced a left-wing Iron cross just wide of his own goal. But when the corner was swung in, referee Nigel Lugg spotted a push by a Fleet player and Davis smashed the penalty home on his 200th appearance for Braintree.
Before the second half started, Day was escorted across the pitch by a steward to take a seat in the main stand - on the opposite side of the ground to the dugouts.
Stuart Lewis tried his luck from distance but Hamann pulled off a routine save.
Kedwell then went close twice in a minute, first heading over from Stuart Lewis' corner and then shooting over from a Theo Lewis cutback. Kedwell and his team-mates were adamant they should have had a corner for the latter effort but the officials disagreed.
Ebbsfleet were well on top at this stage, pushing Braintree back time and again.
Stuart Lewis swung over another corner from the left and Clark hit the crossbar from point-blank range. Johnson headed over from Lewis' next set-piece as the onslaught continued.
The hosts did come into the game more in the closing stages but neither side could find a late winner.
Braintree: Hamann, Peters, Clerima, Masey, Habergham, Paine, Isaac, Davis, Sparkes (Walker 70mins), Akinola, Cox (Marks 61mins). Subs not used: Brundle, Maybanks, Pentney.
Ebbsfleet: Edwards, Fish, Langmead, Acheampong, Clark, Howe (Kiernan 26mins), S Lewis, Johnson, T Lewis, Kedwell, Cunnington. Subs not used: Hall, Pooley, Shields, Day.
Attendance: 404.