Latics 'keeper Mathew Hudson was in form, making saves to deny Omari Sterling-James, Rakish Bingham and Toby Edser.
Edser also shot wide and ex-Latics Dominic Poleon went close as Ebbsfleet applied further pressure in the second half.
At the other end, Mark Cousins kept out an effort from James Norwood and Mike Fondop shot wide late on.
Latics boss Micky Mellon said after the game: "It was a real battle.
"A difficult game for both sides, both sets of players giving it everything.
"You've just got to take what you get out of it, look for the positives and work on the things you can get better at."
Latics are next in action on Tuesday week, February 13, when they host Boreham Wood.
