A goal in each half from Brendan Kiernan helped Town to a third win in a row and up to 10th in the National League table.
Two clever finishes in front of the BT Sport cameras and a solid defensive display mean Town extend their current unbeaten run to five matches.
Captain Josh Falkingham returned to the Town side after a month on the sidelines, replacing the injured George Thomson.
Muldoon and strike partner Mark Beck then both had glimpes of goal as Muldoon stabbed at George Smith's low cross, forcing Holmes to save, with Beck's overhead kick on the follow up going wide.
Ryan Fallowfield was next to try his luck in a fast paced opening 25 minutes, breaking into the box and getting on the end of Alex Bradley's pull back, though like his teammates was unable to find a way past Holmes, with Warren Burrell's follow up deflected behind for a corner.
The visitors first sight of goal arrived in the 31st minute as Alex Reid picked the pocket of Fallowfield and sent a fierce effort swirling past the top left corner.
Town broke the deadlock five minutes before the break when Alex Bradley's though ball found Kiernan, who was able to round the 'keeper and slide the ball into the net.
It was Ebbsfleet who started the second half the brighter of the two, though James Belshaw showed his quality to tip Chigozie Ugwu's strike over, before Frankie Sutherland shot wide.
Despite the early pressure, Town doubled their lead in the 59th minute as Kiernan headed home Fallowfield's deflected cross and claimed his second of the game.
The visitors still posed a threat at two goals down, with Myles Weston looking lively on the right and shooting narrowly wide after a penetrating run.
With Will Smith and Connor Hall not giving anything up, Ebbsfleet couldn't get on the score sheet as Town secured victory and a fourth clean sheet in five matches.
Harrogate Town: Belshaw, Fallowfield, G Smith, Falkingham, Burrell, Beck, Kiernan (Diamond 85), Bradley, Muldoon, Hall, W Smith
Subs not used: Emmett, Cracknell, Stead, Brown
Goals: Kiernan 40, 59
Ebbsfleet: Holmes, King, Wilson, Ugwe, Weston, Grimes, Egan (Adeloye 67), Sutherland (Obileye 78), Cordner, Reid, Payne
Subs not used: Palmer, Achuba, Biabi
Referee: D Richardson
Attendance: 742 (47 away)