Daniel Wright's second-half winner earned Histon their first league win this year and kept alive their outside hopes of a play-off place.
But the visitors had to wait until the 72nd minute before Michael Frew jinked his way through the Fleet defence and crossed for Wright to side-foot home.
Andrew Tidswell was denied a second goal when his right-foot drive come back off the bar in the final minute.
The win leaves Histon 13 points behind the Blue Square Premier play-off pack.
Ebbsfleet boss Liam Daish told BBC Radio Kent:
"We said it's going to be one of those games where concentration makes the difference. We had plenty of play and plenty of chances.
"The only thing missing was a goal. But we move on and mustn't let the disappointment last too long."
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