Ian Hardman’s 54th minute touchdown sparked the decisive scoring burst as Rovers repeated their home league win over Oldham earlier this season.
The only setback for Featherstone was the loss of prop Andy Bostock with a broken hand. Three times Challenge Cup winners Rovers took an 11th minute lead when centre Josh Hardcastle scored the first of his two tries by plunging over from close range.
On-loan Cory Aston converted and his pass then saw Richard Moore force his way over.
Rovers centre Chris Ulugia was sin-binned in the 27th minute for holding down George Tyson.
Twelve-man Rovers defended excellently to retain their 10-0 lead until half-time but Oldham finally opened their account in the 43rd minute when Richard Leopri put in Scott Turner.
Oldham then missed another chance when Tyson failed to gather the ball near the try line and they were punished when Rovers quickly broke upfield, Uugia sending in Hardman for a superb try.
The home side quickly stretched their lead when Aston set up tries for James Lockwood and Hardcastle.
They rounded things off when Misi Taulapapa made the opening for John Davies to score their sixth try 10 minutes from time.
Rovers coach Jon Sharp said: “We began to play on the front foot in the second-half and things started to open up for us.”
Featherstone Rovers: Hardman; Turner, Taulapapa, Ulugia, Hardcastle; Wildie, Aston; Moore, Carlile, Cooper, Knowles, Davies, Lockwood. Subs: Day, Griffin, Bostock, Tagg.
Oldham: Lepori; Clay, Tyson, Grimshaw, Turner; Leatherbarrow, Hewitt; Neal, Hughes, Burke, Bent, Langtree, Thompson. Subs: Ward, Davies, Owen, Gee.
Referee: Tom Grant (Leeds).
Barrow winger Luke Cresswell grabbed four in his side’s 50-28 fifth round win over fellow League 1 club York City Knights at Bootham Crescent.