After an even start two tries in a four-minute spell, from Craig Ashall and Wayne Reittie, plus a Steve Tyrer goal saw Halifax 10-0 ahead after 12 minutes.
The Rams responded well with Ayden Faal, Rob Spicer and Dwayne Barker all going close but Halifax stretched their lead three minutes before the break with a Sean Penkywicz try.
Six minutes intio the second half Fax's Anthony Bowman crossed and Tyrer converted while a 61st minute try from Adam Robinson saw the visitors into a 24-0 lead.
The Rams' efforts reaped reward after 68 minutes with a try from their best player, Steve Crossley, which Pat Walker converted but Halifax sealed victory late on as Tyrer converted tries from Anthony Thackeray and Paul Handforth.
The Rams' line-up did not include Castleford Tigers utility forward John Davies who has joined Dewsbury on dual registration.
For all the latest news from the Rams see Friday's Reporter.