Halifax wasted little time before taking the lead through Danny Schofield, who made ground inside the penalty area before driving the ball into the bottom corner.
Adam Smith almost added a quick-fire second, but Wrexham were playing some good football, with top goalscorer Moult at the centre of the majority of their attacks.
Five minutes after the restart, Halifax were reduced to 10 men after Marc Roberts was sent off for hauling down Moult when through on goal, and it took just eight minutes for Wrexham to make use of the man advantage.
Neil Ashton delivered a cross from the flank for Moult to power home the header, but parity lasted just two minutes as the Shaymen restored their slender advantage.
Wrexham lost their concentration in defence and Danny Hattersley was perfectly placed to tap home at the back post to put the Yorkshire side back on track for second place.
However, with six minutes to go, some neat work from Andy Bishop helped set up Moult, who made no mistake from close range to earn his team a deserved point.