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Two goals in the last nine minutes kept the Fleet's title challenge on track.
They had trailed to a 53rd-minute Dayle Grubb free-kick until skipper Danny Kedwell and susbtitute Darren McQueen came to Ebbsfleet's rescue.
It means the Fleet remain a point behind leaders Maidenhead, who won comfortably at home to Welling.
Not surprisingly for a team with 10 wins and a draw in their last 11 league games, Fleet boss Daryl McMahon named an unchanged team.
It meant that key midfielder Andy Drury was fit despite picking up an ankle injury last weekend. Anthony Cook (illness) and Jack Connors (hamstring) were also passed fit.
Loan signing Jake Howells, who joined from Dagenham as cover on Thursday, did not even make the bench for the Fleet.
Fleet made all the early running with wideman Cook and Sam Deering at the fore.
Indeed, Deering had the best chance of the half inside just four minutes. Weston keeper Luke Purnell hit his clearance straight to Deering, who wastefully dragged his left-foot shot wide of the near post.
Cook went closer on 17 minutes, robbing Lloyd Humphries of the ball before sending a right--foot shot against the inside of the upright from the edge of the penalty area.
Weston weathered the early Fleet storm, though, and grew into the game the longer the first half went on and skipper Grubb twice threatened from distance.
Referee Alan Dale booked Rollin Menayese for taking out Deering and then Jake Lee on the stroke of half-time for a late foul on Marvin McCoy.
Weston took a shock lead eight minutes into the second half when dangerman Grubb's free-kick somehow found its way past Ashmore from 30 yards.
It could have been worse for Fleet had Cook not been on hand to clear off the line on the hour mark to deny Menayese after Ashmore dropped a long free-kick.
Fleet were creating nothing and it needed triple substitution to get them going as on came Dean Rance, Sean Shields and McQueen.
Kenny Clark and Cook both went close before, with time running out, Kedwell came to the Fleet's rescue on his 100th appearance for the club.
Collecting the ball with his back to goal, Kedwell turned his marker and fired low brilliantly beyond Purnell from 25 yards for his 10th goal of the season on 81 minutes.
Three minutes later, the Fleet were ahead. Shields' deep cross was headed down by Kedwell and McQueen nodded home to send Stonebridge Road wild.
Ebbsfleet: Ashmore, Cook, Connors (Shields 67mins), McCoy, Phillips, Clark, Powell (Rance 67mins), Drury, Kedwell, Bubb (McQueen 67mins), Deering. Subs not used: Mambo, Jordan.
Weston: Purnell, Pope, Greenslade, Humphries (Reid 87mins), Baldwin, Menayese, Chemlal (Kingston 64mins), Cane, Ash, Grubb, Lee (Hill 87mins). Subs not used: Laird, Barker.
Atttendance: 1,325.