After an awful start, the Shaymen produced some good football and another hard-working, disciplined display, limiting the hosts to few clear chances.
Manager Billy Heath was keen to see Halifax keep a clean sheet on the road again after doing so in their first five away games, but his side were caught napping when, after a foul by Matty Kosylo, Bruno Andrade went for goal when everyone must surely have been expecting a cross, and beat goalkeeper Sam Johnson at his near post.
Portuguese Andrade, the hosts’ biggest threat by far, had the ball in the net again, but his strike was ruled out for offside, although Heath was not happy that Johnson had parried Dan Holman’s shot straight into his path after the visitors had stood off.
Thankfully for the Shaymen, the visitors weathered the early pressure and worked their way into the game.
Kosylo was Halifax’s brightest spark and he enjoyed his free role in a 3-5-2 formation behind Ben Tomlinson, making his first start since the opening day, and Tom Denton, twice testing Grant Smith from long range.
Holman and Keiran Murtagh both went close with headers from inside the area as Halifax’s threat tapered off.
But, after Kosylo’s shot across goal was only parried by Smith, Morgan was left with a tap-in to equalise.
The goal came before Denton was dismissed for an alleged elbow on Stephens.
Boreham Wood: G Smith, K Smith, Stephens, Wells, Woodards, Ricketts, Shakes, Champion, Murtagh, Andrade, Holman (Benson 75). Unused substitutes: Jeffers, Turley, Thomas, Turgott.
FC Halifax Town: Johnson, Moyo, Brown, Hotte, Wilde, McManus, Oliver, Lynch (King (81), Kosylo (Clarke 90), Tomlinson (Morgan 75), Denton. Unused substitutes: Nicholson, Macdonald.
Referee: C Brook.