Town made the early running as Brendan Kiernan cut inside from the left wing and had his shot saved, before a short back pass almost put Jack Muldoon through on goal, but Jordan Holmes was quick off his line to clear.
Town broke the deadlock five minutes before the break when Alex Bradley’s through ball found Kiernan, who was able to round the goalkeeper and slide the ball into the net.
Ebbsfleet started the stronger of the two sides in the second half and James Belshaw showed his quality to tip Chigozie Ugwu’s strike over, before Frankie Sutherland shot wide of the goal.
Despite the Ebbsfleet pressure, Town doubled their lead in the 59th minute as Kiernan headed home Fallowfield’s deflected cross and claimed his second of the game.
What is happening to former Leeds United star Raphinha at Barcelona amid latest farce and deadline
Leeds United plot ‘double hit’ for attacking duo, Whites ‘weighing up’ bargain defender swoop
Leeds United news: Raphinha set to miss La Liga opener as Whites eye MLS left-back
Leeds United ‘express interest’ in transfer as ‘decision made’ over player’s future
Leeds United in ‘direct talks’ over swoop for rising star as Jesse Marsch makes ‘transfer decision’
The visitors did not give up however and Myles Weston had the best of their chances when he shot narrowly wide after a impressive run but Town held on to claim victory and their fourth clean sheet in five matches.
Meanwhile, Liam McAlinden’s first-minute goal saw FC Halifax Town move back to the top of the National League as they beat Maidenhead 1-0.
McAlinden struck less than 45 seconds into the first half when the ball broke to him on the edge of the box, and his sweetly-struck left-foot shot arrowed across goal into the bottom corner for his seventh of the season.
After his low shot from a corner was saved by Chris Dunn, Tobi Sho-Silva brought a fine save from the keeper before the same player sent two decent chances over the bar, one a flick header from a right-wing cross, and the other an awkwardly-struck shot from the left of the area after a cut-back.
Substitute Jeff King could have sealed it late on for Town but Dunn saved his shot across goal, before Sam Johnson was finally tested, keeping out a fizzing drive from substitute James Akintunde.
Tadcaster Albion moved into second spot in the BetVictor League North West Division after a 1-0 victory at Widnes.
The only goal of the game came from Jacob Day on 33 minutes and the win moved Albion to within five points of league leaders Workington with four games in hand.
A first-minute goal from Vaughan Redford proved enough for Pontefract Collieries to defeat Runcorn Linnetts 1-0 which moved the West Yorkshire side up to fifth place in the league.
Fourteenth-placed Brighouse Town meanwhile went down 2-0 at Ramsbottom United while 17th-placed Ossett United suffered last-minute heartbreak when they went down to a 90th-minute winner at City of Liverpool.
In the South East Division, Frickley Athletic suffered a 5-1 thrashing at the hands of Stamford. Jacob Hazel netted for Frickley.
In the Northern Counties East League Premier Division, Liversedge moved up to fifth place thanks to a 3-1 victory at Silsden. After falling behind early on, Alfie Raw, Michael Bottomley and Kevy Tarangadzo found the net for Liversedge who chalked up their fifth win in seven matches.
Fourth-placed Hemsworth MW drew 1-1 at Penistone Church with Nash Connolly getting on the scoresheet.
Seventh-placed Yorkshire Amateur drew 1-1 at home Bridlington Town.
Ashley Flynn gave the home side the lead only for Josh Greening to equalise for Town.
Elsewhere, Knaresborough Town lost 1-0 at home to Albion Sports and Garforth Town were humbled 6-1 at home to leaders Grimsby Borough.
In Division One, a brace from Chris Jackson helped Selby Town beat Ollerton Town 4-1, Nostell MW lost 3-2 at Hallam, Harrogate Railway were hammered 5-0 at North Ferriby while Glasshoughton Welfare were 2-1 winners at Worsbrough Bridge.