On-loan Matthew Godden scored the winner on his debut as Ebbsfleet battled back from two goals down to beat fellow strugglers Hyde.
The visitors raced into a two-goal lead through Richard Crowther and Nick Blinkhorn before Neil Barrett headed the hosts back into it.
Nathan Elder volleyed the Fleet level after the break.
But Ashley Carew then played in substitute Godden who slotted past visiting keeper Christopher Dilo.
VIEW FROM THE DRESSING ROOM
Ebbsfleet manager Liam Daish told BBC Radio Kent:
"I thought we were shocking (at first), but to go 2-0 down at home it's very difficult, and for the supporters that transports onto the pitch.
"We got a lifeline, came in just a goal down and in the second half we scored two goals and the lads that came on made a big difference.
"I'm just pleased we got three points in a massive game against a team who beat Grimsby and Cambridge of late and their front runners were a handful today.
"We've got the three points, in the paper it says 3-2 to Ebbsfleet, we'll talk about why we started like that. Slowly but surely we peaked at the end to score the winner."