McLeod was on target along with Shaun Williams and 17-year-old substitute Brendan Galloway - for whom it was his first career goal - while Lee Gregory replied for the Shaymen.
Halifax frustrated the Dons early on but McLeod broke their resistance six minutes before the break when he curled a fine left-footed shot into the top corner from 25 yards.
Dan Gardner missed a golden opportunity to equalise for Halifax on the stroke of half-time when he was denied one-on-one by goalkeeper Ian McLoughlin after bursting clear of Lee Hodson.
And Williams doubled the Dons' lead eight minutes after the break, sending Matt Glennon the wrong way from the penalty spot after Daniel Powell had been tripped in the box by Marc Roberts.
Halifax rallied but McLeod made it three-nil after 70 minutes when he rammed in the rebound after Glennon had parried substitute George Baldock's curling shot.
Gregory pulled a goal back for the Shaymen in the 78th minute when he finished well from a tight angle, before Galloway rounded Glennon to slot home the Dons' fourth goal at the close.