The Shaymen took the lead early on through Aaron Martin, getting his first for the club, but the sending off for Jack Senior changed the tempo of the match.
Elisha Sam's responded with a thunderous strike, but the Pies will be frustrated not to take three points following the heroics of Halifax goalkeeper Sam Johnson.
These two sides had faced each other as recent as just over a week a go in FA Trophy action, which saw Notts County advance thanks to a stern 2-1 victory.
Burchnall named an unchanged side from his team's victory over Eastleigh on Saturday, meaning Matty Palmer's record of not missing a minute this season continues.
Notts County: Jaros; Richardson, Brindley, Cameron, Chicksen, Francis, Palmer, Rodrigues, Sam, Roberts, Wootton
Halifax manager Pete Wild did opt to alter his team however, making two changes as Kian Spence and captain Niall Maher replaced an injured Matty Warburton and Tyrell Warren.
Halifax Town: Johnson; Debrah, Bradbury, Maher, Senior, Summerfield, Woods, Allen, Spence, Martin, Waters
Shots on target: 9-1
Shots off target: 13-0
Yellow cards: 1-3
Red cards: 0-1
Story of the match
Notts County head coach Ian Burchnall had been full of praise for his side and wasn't dwindled by the weight of the fixture, so he will have been delighted with his team's first half.
Supporters were left shocked when a corner fell to Richard Brindley from six yards out, but the defender failed to adjust himself and smashed over the bar.
But with Notts County dominating and looking the more likely to find the breakthrough, Halifax pounced on a chance and counter-attacked, allowing Martin to round Vitezslav Jaros in goal before rolling the ball into the empty net, getting his first for the Shaymen.
With the Pies trailing, Sam took aim from distance and rattled Johnson's post to the agony of the home supporters.
Halifax would be struck a major blow however, as defender Senior was shown a second yellow card for an off-the-ball incident with Cal Roberts, resulting in the Shaymen being reduced to ten men.
And on the brink of half-time, Notts County would take advantage, as Sam netted his third of the campaign. A searching ball found the Belgian, who cut inside of his man before hammering a strike past a stranded Johnson.
Heading into the second half, Notts County looked to carry their dominance and did so, as Adam Chicksen created a yard of space for himself but his effort was smothered by Johnson.
Rodrigues was up next to ponder the idea of a goal, as his long-ranged effort forced a reactive stop from Johnson.
Frustrations for County
A point before the match wouldn't have been the worst result in the world for Notts County, their performance deserved the three points.
The dismissal of Senior completely changed the tempo of the match, but a lack of attacking prowess is what has eventually punished County, and we'll have to wait and see how detrimental it could be in their season.
Before the sending off of Senior, the Shaymen were looking dangerous on the attack and like they could nick the three points.
However, Senior's sending off changed the entire flow of the game, and defensively Halifax were solid and the defenders will deserve a well-earned rest after today's performance. In particular Johnson, who was brilliant.
Belgian forward Sam used his physical presence to be a nuisance to the Halifax defence right from kick-off, and was unfortunate only to get the one goal.
His solo strike was expertly converted and showed his class, and Burchnall may have uncovered something using Sam on the wing rather than as a target man.