Fax, who have not been in the quarter finals since 2002, had young centre Chester Butler and wing James Saltonstall in two-try form as they registered a third straight win under caretaker coach Simon Grix.
Lee Greenwood’s Rams were never really in the game after going 12-0 down inside the opening 10 minutes, with Fax leading 18-6 at the break before closing things out in the second half.
The visitors took the early lead, the hugely talented Butler trampling Adam Ryder to score on the right after James Woodburn-Hall and Scott Murrell had shipped the ball wide.
Centre Steve Tyrer converted from the sideline and the Rams found themselves reduced to 12 men temporarily when Liam Finn was sin binned for trying to delay the restart after Scott Murrell’s raking 40/20 kick.
Halifax made them pay immediately, Woodburn-Hall exploiting some awful defence on the goalline to score his side’s second try, Tyrer converting.
And Fax added to their tally with a third score on 22 minutes, back rower Ed Barber’s perfectly judged kick putting the ball on the plate for Saltonstall to touch down, Tyrer again on target from the touchline as the lead stretched to 18-0.
The Rams needed some inspiration and they finally got it on the half hour, centre Lucas Walshaw forcing his way over from close range and Finn adding the extras to keep them in touch at the break.
But it was Fax who extended their lead after the restart, an awful error from Andy Gabriel gifting them an attacking position and Butler scoring his second try from Murrell’s cross kick.
Tyrer’s conversion attempt went wide to leave the score at 22-6 but when a brilliant kick from Ben White coaxed an equally excellent finish from winger Shaun Robinson, Tyrer was on target as the visitors moved into a decisive lead at 28-6 with 25 minutes remaining.
The rest of the evening was largely uneventful, with the visitors never really threatening to cut loose, but a Rams revival an equally distant prospect.
The visitors’ quarter final spot was confirmed by Saltonstall’s late, unconverted, try and White’s last-play penalty.