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Ebbsfleet climbed to third in Skrill South with a 1-0 win at Farnborough on Tuesday night.
The visitors, who arrived in Hampshire on the back of three straight defeats, were not at their best but they showed real resilience once Bricknell had put them ahead on 69 minutes.
Farnborough piled on the pressure in the closing stages but the Fleet held on for a precious win which lifted them above promotion rivals Sutton.
In the only change to the Ebbsfleet side which started Saturday's 1-0 FA Trophy defeat at Havant & Waterlooville, Ben May came in for Michael Thalassitis up front.
Former Fleet striker Moses Ashikodi, meanwhile, started for Farnborough.
The visitors almost went ahead inside three minutes, Michael West heading Aiden Palmer's left-wing delivery back across goal but the wrong side of the far post.
A Daryl McMahon free-kick then bounced just in front of Boro keeper Dan Lincoln, who did well to hold onto the ball when it reached him.
Farnborough were slow out of the blocks although they did have their moments, including when Adam Doyle collected Phil Page's pass and fired a shot wide.
But the Fleet looked the more likely scorers for much of the first half.
Anthony Cook was their main threat and he went close three times. The winger fired one shot wide, saw a second effort deflect behind off one of his team-mates and then swung over a cross-shot which Lincoln gathered on the stretch.
May got up well to meet a floated Palmer free-kick but his header was straight at Lincoln, who gathered easily.
Steve Brown's side were dominating possession but lacked a cutting edge.
And they almost conceded just before the interval when Josh Huggins met Page's corner from the left with a glancing header which flashed across goal.
The second half started at a good tempo and both sides carved out decent chances.
Bricknell connected with Palmer's low centre and his shot was heading on target when it was blocked by a Farnborough defender.
But there was a moment of real danger for the visitors when Daniel Bennett, having mis-kicked from six yards, got a second bite at the cherry. Edwards clawed his stabbed shot out and then denied Ashikodi, who was looking to bundle in the rebound.
Ebbsfleet had come out for the second half with plenty of intent but still they lacked composure on the ball. And when they didn't have it, there was a nervousness about their defending.
But just as the game appeared to be drifting away from them, a goal came.
Palmer played a low ball into the box and it fell at the feet of Bricknell, who turned sharply and arrowed a fine shot into the bottom corner.
The home side's response was immediate and suddenly the Fleet were on the back foot, heading and blocking a flurry of high balls.
Page got a yard of space and was just about to pull the trigger when Paul Lorraine came to Ebbsfleet's rescue with a magnificent sliding block.
The Fleet had to withstand a late bombardment and Bennett had a great chance to equalise after an almighty goalmouth scramble, but the visitors held on.
Farnborough: Lincoln, Huggins, Treacher, Bosch, Inns, Doyle (Siaw 80mins), Bennett, James-Lewis (Jeffrey 77mins), Page, Ashikodi (Hammond 77mins), Berry. Subs not used: Fearn, Scriven.
Ebbsfleet: Edwards, Sessegnon (Howe 80mins), Lorraine, Sankofa, Palmer, West (Osborn 68mins), McMahon, Rance, Cook, May, Bricknell (Corcoran 84mins). Subs not used: Hall, Thalassitis.
Attendance: 219.