Ben Heaton's try put the visitors ahead before John Davies and Scott Turner went over to help give Featherstone a 13-6 half-time lead.
Turner grabbed his second try before Ben Johnston jinxed his way through to reduce the deficit for Halifax.
Anthony Thackeray kicked his second drop goal of the night and Josh Hardcastle's try made the game safe.
In the battle of the two Championship sides, Scott Murrell sent Heaton clear to put Halifax ahead, but the lead only lasted four minutes as Keal Carlile spun out of a tackle to set up Davies.
A brilliant finish from Turner and Thackeray's drop goal on the stroke of half-time gave the hosts a seven-point lead.
Turner cleverly grounded the ball in the corner for his second try, but Halifax hit back with a fine solo try from Johnston.
Hardcastle went over from the scrum with seven minutes remaining as Featherstone became the first team in reach the quarter-finals.
Featherstone: Hardman, Turner, Ulugia, Taulapapa, Briscoe, Thackeray, Aston, Moore, Carlile, Cooper, Knowles, Davies, Lockwood.
Replacements: Wildie, Griffin, Tagg, Hardcastle.
Halifax: Sharp, Saltonstall, Woodburn-Hall, Tyrer, Worrincy, Murrell, Robinson, Tangata, B. Moore, Cahalane, Grady, Heaton, Fairbank.
Replacements: Morris, Boyle, Barber, Johnston.
Referee: Chris Campbell (RFL).
Featherstone beat Halifax to reach the Challenge Cup quarter-finals for the first time in 20 years.