The Shaymen had drawn seven and lost five league matches since beating Gateshead 1-0 on August 27,
That win sent them top of the table; the prospect of a near three-month wait for their next league win that day will have seemed fanciful.
But Dover was the day that run finally ended. Town have certainly played better and not won since then.
Dover’s record heading into the game - two wins out of 19 in the league and no wins away, as well as the second worst defensive record - made a Town win even more of a necessity, although the National League’s bottom side eventually got into the game to push Town all the way.
It wasn’t pretty for the most part, but points took precedence over performance given the winless run The Shaymen were on, and the overdue victory is just what Town needed heading into the cup replay with Morecambe on Tuesday.
Kevin Lokko headed over from a free-kick 10 minutes in, but that was all the visitors mustered in the first-half.
Dover were generally happy to sit back and let Town try to break them down, but the division’s bottom side looked a team low on confidence, making no impression on the Halifax defence.
Town were trying - as evidenced by Josh Staunton putting his head where it hurt when lying on the ground trying to regain possession nearly the halfway line - but didn’t have the quality or tempo required early on.
Dayle Southwell chased the ball tigerishly around the Dover defence, while Jacob Hanson was again full of running down the right.
But Town’s pressing was sporadic, as were their attacks. The hosts saw more of the ball, but it took Halifax a fair while to warm up amid a slow start.
The Shaymen had a couple of corners and the odd individual burst towards the box, but not enough to cause any real excitement.
There was little space for the likes of Kosylo and Cameron King to influence proceedings, while Southwell had little chance in the air against Dover’s height at the back.
Although the visitors hardly radiated composure or poise, there was no spark of creativity to really fire Town into life.
Kosylo’s goal was just what they needed though after a scrappy display up to that point, as his shot from the edge of the box found the top left corner with the aid of a very welcome deflection.
Town should have doubled their lead when King’s deft touch played Southwell in on goal at an angle, but his venomous shot crashed off the bar.
Southwell nearly set-up a second shortly after the interval with a terrific run and cross that was helped on by King to Kosylo, but his prod goalwards rolled just wide.
An individual error threatened to derail Town again when Niall Maher gave the ball away inside his own half, but Jamie Allen’s poor cross was caught by Sam Johnson.
Southwell and Inih Effiong then traded chances, with both shots at an angle kept out, before Effiong miscued a shot wide from Dover’s next attack.
The visitors were enjoying their best spell of the game, putting Town under more pressure than they had in the entire first-half.
The Shaymen needed a second goal to calm the nerves, with Stuart Lewis thundering a shot just over the bar from Johnson’s punch clear, before Effiong got a couple more sniffs of goal.
The second nearly came through an own goal from Southwell’s cross, but Mitch Walker kept out the inadvertent touch from his team-mate.
The Shay held its collective breath when Johnson kept out a low shot amid some late pressure.
Halifax: Johnson, Hanson, Brown, Clarke, Skarz, Maher, Staunton, Odelusi (Preston 61), King (McLeod 89), Kosylo, Southwell (Edwards 83). Subs not used: Rowley, Sellers.
Scorer: Kosylo (39)
Shots on target: 3
Shots off target: 6
Dover: Walker, Passley, Lokko, Brundle, Allen, Effiong, Gomis (Nortey 67), Lewis, Debayo, Taylor, Reason (Diarra 84). Subs not used: Adebowale, Worgan, Huckle.
Shots on target: 3
Shots off target: 6
Referee: Rebecca Welch
Town man of the match: Cameron King