Richard Marshall’s side overcame an 8-0 deficit to lead 10-8 at the break and never looked in danger to maintain their top-four challenge.
Neither side was overly creative during the opening quarter, although what half chances there were fell Halifax’s way, with Ben Heaton and Ben Johnston both breaking the line without managing to find support.
Ironically, after struggling for field position for lengthy spells, it was Dewsbury who finally breached the line just before the half hour, Scott Hale running onto an Andy Kain pass to score.
Paul Sykes could not add the conversion, but the Rams were in again before Halifax had touched the ball, Sykes kicking across the field and winger Dale Morton claiming the try.
Sykes’s sideline kick drifted wide, but at 8-0 the Rams looked handily placed.
But a Gareth Moore kick and chase on the last tackle saw the half back open Halifax’s account, centre Steve Tyrer converting from close to touch.
And the visitors claimed a lead they just about merited, Scott Murrell kicking wide and James Saltonstall leaping high to claim the ball and the try. Tyrer’s kick drifted just wide, but the teams went to the break at 10-8.
Halifax extended their lead, Connor Robinson slipping Mitch Cahalane under the posts and Tyrer converting for a 16-8 advantage.
The visitors added a penalty with 18 minutes to go, Tyrer tapping it over after Simon Grix had threatened on the left.
Leading 18-8, the visitors strangled the life out of their hosts in the final quarter with some terrific defence and finally made certain when Robinson kicked, chased and scored with five minutes remaining, Tyrer converting.
Dewsbury: Guzdek; Morton, Crookes, Grady, Grant; Sykes, Kain; Groat, Speakman, Jackson, Hale, Muranka, Adamson. Substitutes: Conroy, Teanby, Pryce, Tonks
Halifax: Johnston; Sharp, Heaton, Tyrer, Saltonstall; G. Moore, Murrell; Cahalane, Kaye, Tangata, Manning, Sarsfield, Fairbank. Substitutes: Robinson, Ambler, Grix, Boyle
Referee: M Woodhead (RFL).