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Bradley Bubb scored twice as the Fleet ensured the National League South title race is not over just yet.
They had to come from behind yet again - conceding first for the sixth time in eight matches.
But four second-half goals mean they trail leaders Maidenhead by five points with just three games to play.
Fleet boss Daryl McMahon made three changes from the team that drew at Truro last weekend.
Danny Kedwell was ruled out with a broken arm while Mark Phillips and Anthony Cook dropped to the bench.
In came Sean Shields, Bradley Bubb and Dave Winfield, who took the captain's armband in Kedwell's absence.
Fleet dominated the opening half-hour in terms of possession but never really had a clear sight of Jordan Holmes' goal. Without Kedwell up front, neither Bubb or Darren McQueen got much change out of a five-man Eastbourne defence.
On 29 minutes, Fleet keeper Nathan Ashmore had to turn behind Ryan Worrall's cross from near the touchline that looked to be heading for the far corner.
Fleet's best opening of the first half came on 36 minutes when neat play in midfield saw Sam Deering feed Bubb, who was tackled as he shaped to shoot by Kieron Khinda-John.
It proved a costly miss as Eastbourne took the lead just two minutes later. Gavin McCallum's shot was beaten away by Ashmore but referee Elliott Kaye pointed to the spot for handball as Kenny Clark controlled the loose ball.
Clark was booked by the referee and Worrall stepped up to put Eastbourne ahead from the penalty spot.
Fleet were on level terms 12 minutes into the second half. Bubb started and finished the move, flicking the ball wide for Deering and then nodding in the cross after McQueen was denied at the near post.
Drury curled a 67th-minute shot against the far post but Fleet went ahead just a minute later.
The increasingly influential Drury sent a perfect pass behind the full-back and Cook fired low past keeper Holmes for his 11th goal of the season.
Drury had a 25-yard shot turned behind by Holmes, who went off injured shortly afterwards - the effects of a challenge by Bubb early in the second half.
Fleet made the points safe with two minutes left when Aaron McLean marked his return from injury by setting up Bubb, who fired into the roof of the net.
It was nearly four but Deering's low shot was saved when he opted to go for goal instead of looking for the unmarked McLean.
But Fleet were not to be denied and it was 4-1 in the 95th minute. Deering was fouled by substitute keeper Lewis Carey and McLean - after a discussion with Bubb who was on a hat-trick - took on penalty duties.
He powered his shot low through the middle of goal to mark his return to first-team action for the first time since September with a goal.
Ebbsfleet: Ashmore, Shields, Connors (Cook 57mins), McCoy, Winfield, Clark, Powell (Rance 73mins), Drury, McQueen (McLean 78mins), Bubb, Deering. Subs not used: Phillips, Jordan.
Eastbourne: Holmes (Carey 73mins), Hare, Stone, Hughes, Simpemba, Hobson, McCallum, Worrall (Oxlade-Chamberlain 75mins), Connolly (Pinney 68mins), Taylor, Khinda-John. Subs not used: Bosma, Tate.
Attendance: 2,477.