Angelo Cappello’s first goal of the season handed Halifax a 1-0 win away to National League basement boys Ebbsfleet.
The visitors needed just three minutes to get their noses in front when Jamie Cooke’s effort was deflected to Cappello, who made no mistake.
Keeper Mark Cousins saved from Andrew Oluwabori and Cooke saw another effort blocked as Town pushed for a second, but their lead remained slim at the break.
Oluwabori fired just wide three minutes after the restart and Ebbsfleet midfielder Jephte Tanga saw appeals for a penalty waved away.
Defender Tom Dallison headed just wide with 13 minutes remaining as the hosts looked for an equaliser but Halifax held on despite Cooke being sent off in stoppage time.