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Ebbsfleet were held to another draw at home on Tuesday night.
They came from behind to lead Havant & Waterlooville 2-1 but couldn't hold on and dropped points at Stonebridge Road for the second time in a week.
Fleet are now 11 points clear at the top of the table but their title rivals Sutton and Maidstone both have three games in hand.
Ebbsfleet came into the game on the back of a disappointing 0-0 draw at home to Hayes & Yeading three days earlier and manager Daryl McMahon made three changes to his line-up.
Left-back Joe Howe started his first game of 2016 and there was also a recall for midfielder John Paul Kissock, while striker Danny Kedwell returned after suspension.
Anthony Cook dropped to a bench which also featured Michael West - back after a loan spell at Whitehawk - but neither Bryan van den Bogaert or Jordan Parkes featured in the Fleet squad and Danny Haynes also had to watch from the stands.
Havant boss Lee Bradbury handed a full debut to James Haran, a loan signing from QPR, but the visitors were otherwise unchanged from their dramatic 2-1 win over Maidstone at the weekend.
They scored two stoppage-time goals to turn that game around and the confidence they'd gleaned was evident in their early play. Ebbsfleet, by contrast, looked nervous and uncertain - no more so than when Havant put balls into their box.
Nic Ciardini saw a shot deflect behind off Dean Rance after Matt Fish and Anthony Acheampong had got themselves into a muddle trying to deal with a cross from the Havant right - but the next delivery saw Fleet fall behind.
Harry Medway, overlapping down the left, floated a cross to the back post and with goalkeeper Brandon Hall caught under the flight of the ball, it dropped inside the upright.
The home side were rocking at that stage and Aaron Mitchell set up Scott Donnelly for a shot which flew across the face of goal.
Ebbsfleet tried to pass their way back into the game although much of their possession football was in front of the Hawks, who packed men behind the ball.
Until, that was, a patient move in the 24th minute saw Matt Godden create a yard of space in the box for Kissock, who showed a cool head to roll the ball inside Young's right-hand post for his first Fleet goal.
The home side's next chance came via a more direct route. A ball over the top sent Rance running through on goal but the defensive midfielder, finding himself in rather unchartered territory, shot straight at Ryan Young.
Stuart Lewis, who like Kissock and Rance came into this game without a goal to his name in 2015-16, sent a half-volley into the Swanscombe End when the ball sat up nicely on the edge of the box.
But for all the Fleet's good work going forward, they still looked edgy at the back. Hall hooked a poor clearance straight to Scott Donnelly, whose lob flew over, before Mullings outmuscled Tom Bonner and drove a shot wide.
Between those half-chances, Ebbsfleet put together a move of real quality and almost took the lead. Lewis won the ball 20 yards from his own goal and fed Kedwell, whose first-time pass sent Godden haring down the right wing. Play was switched to the left and Howe, with Havant players backing off, thumped a shot through the box and just wide.
Mitchell was in the thick of the action at the start of the second half, drilling a shot wide before catching Lewis late and going into referee Colin Lymer's notebook.
At the other end, Kedwell tried his luck with a free-kick 30 yards out but his low shot lacked the power to beat Young.
But the Hawks keeper was beaten for a second time on 54 minutes. Howe's hanging cross from the left reached Godden, who climbed superbly and planted a textbook downward header into the net for his 20th goal of the season.
Kedwell almost made it 3-1 with a glancing header from Lewis' whipped free-kick and Rance then led a fine break when he surged over the halfway line. Rance fed Godden and he swapped passes with Kedwell before driving the ball into the net - only to see the flag raised for offside.
But the scores were level on 74 minutes. Matt Fish carelessly gave the ball away in midfield and when Havant broke, substitute James Hayter touched home Mitchell's low cross from the left.
Fleet looked to respond and McLean went close twice in a minute, firing Godden's cutback against a defender and then heading wide from the resulting corner.
But a Ciardini free-kick dropped inches wide at the other end as the nerves returned for Ebbsfleet and their supporters.
McMahon sent Charlie Sheringham on for the last eight minutes and Lewis hooked a shot wide when Havant failed to clear Howe's left-wing cross.
But that was the Fleet's last chance as Havant, who had Haran sent-off in stoppage-time, held on for a crucial point in their bid to stay in the division.
Ebbsfleet: Hall, Fish, Howe, Lewis, Acheampong, Bonner, Rance, Godden, Kedwell, McLean (Sheringham 82mins), Kissock (West 90mins). Subs not used: Clark, Miles, Cook.
Havant: Young, Strugnell (Hayter 67mins), Medway, Stock, Haran, Hill, Swallow, Donnelly, Mullings, Ciardini, Mitchell (Thompson 84mins). Subs not used: Cummings, Paterson, Blanchett.
Attendance: 854.