Hulme nodded home on 31 minutes to seal the win for the Division One promotion hopefuls against CMB.
The win, at the County Ground, Leyland, was the club's third higher division scalp in this year's competition after wins against Blackpool Wren Rovers and Slyne-with-Hest.
Hulme struck after a goalmouth scramble to be the difference in a cagey match with few chances.
It follows their Challenge Cup victory last season and could be a platform to earn promotion to the Premier Division next season.
They have six league games left to play with a potentially title battle looming at Lostock St Gerards on the final game of the season.
CMB meanwhile still hope to haul in Burscough Richmond at the top of the Premier Division with four games left to play.
ROSSENDALE'S ROUTE TO THE TROPHY
Round 1
3-1 Hesketh Bank (h)
Round 2
1-0 Haslingden St Mary’s (h)
Round 3
6-1 Charnock Richard Res (a)
Quarter-final
3-0 Blackpool Wren Rovers (a)
Semi-final
4-2 Slyne-with-Hest
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