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Ebbsfleet dropped points against a promotion rival for the second time in four days at Stonebridge Road.
Despite taking an early lead, Fleet showed plenty of nerves before Hampton claimed a deserved point with a late equaliser.
It means the Fleet now trail leaders Maidenhead by 10 points.
Fleet came into the game on the back of a 3-2 defeat to leaders Maidenhead on Saturday. Boss Daryl McMahon dropped Sam Deering and Darren McQueen, bringing in Jack Connors and Bradley Bubb in a 4-4-2 formation.
It was Bubb who got the Fleet off to the perfect start. Indecision in the Hampton defence saw keeper Billy Bishop's clearance hit his own defender and Bubb was on hand to calmly slot home the loose ball.
Fleet had the better chances early on. Dean Rance fired over from distance, Bubb forced Bishop to turn his shot behind and from the resulting corner Danny Kedwell headed narrowly over the bar.
It took Hampton 25 minutes to have a sight of Nathan Ashmore's goal but ex-Fleet man Brendan Kiernan shot high and wide.
Kedwell missed his kick just in front of goal on 40 minutes but Hampton should have levelled a minute before the break.
After Ashmore's double save, the ball went around the Fleet area like a pinball, Kenny Clark blocking one effort, Kiernan hitting the post and Nicke Kabamba shooting wide when it seemed easier to score.
Hampton carried on where they left off after the break. Portsmouth-bound Jamal Lowe shot over before a mazy run ended when his effort was deflected wide for a corner.
It needed another smart save from Ashmore to deny Christian Jolley, the Fleet keeper then saving from Jack Taylor with his Fleet.
It was not just the shot-stopping that Ashmore excelled with. His handling with impeccable and as the Fleet sat deeper and deeper he relieved the pressure by taking every cross with ease.
Kiernan's shot clipped the bar late on and just when it looked like Fleet would get through to the final whistle, Hampton were level.
A corner - needlessly conceded by Powell's wayward clearance - was not cleared and Lowe was on hand to drill in an 89th-minute equaliser.
Hampton nearly snatched it at the death but Fleet somehow got bodies in the way as they struggled to clear and Kabamba sliced over from close range.
Ebbsfleet: Ashmore, Cook, Connors, Phillips, McCoy, Clark, Rance, Shields (Deering 58mins), Kedwell (Sheringham 74mins), Bubb, Powell (McQueen 89mins). Subs: Miles, John.
Hampton: Bishop, Jelley, Casey, Kamara, Collier, Odametey, Kiernan, Taylor, Kabamba, Lowe, Jolley. Subs: Murphy, Howe, Hippolyte-Patrick, Gasson, Williams.
Attendance: 828.