Featherstone became the first team to defeat Sheffield by more than 12 points all season in the first round of the play-offs.
Rovers silenced the home support at the Don Valley Stadium to book a trip to Widnes next weekend.
In a fiesty first half, converted tries by Kyle Briggs and Tim Spears, plus a Iestyn Harris penalty gave the visitors a 14-0 lead. Jonny Woodcock pulled a penalty back for the Eagles on the stroke of half time.
Tommy Saxton‘s try earlier in the second half edged Rovers to 18-2 and in a commanding position.
Rovers travel to Widnes, 26-21 victors over Whitehaven on Thursday, on Friday for an 8pm kick-off at the Stobart Stadium.