Scorers were Lawrence Read (2), Dave Easterby, Dan Tyrer and substitute Chris Bibby.
Holders Rimington then found it hard work against a Sedbergh side, who defended well but lacked a finishing touch.
Once Rimington took the lead after the break, they gained control with three well-taken goals through Glen Dinsdale (2) and Matt Baygot to book their place in the final.
Hellifield Sports are still waiting for their opposition in the Morrison Cup final tomorrow night at Skipton Town AFC as Cononley Sports and Grassington Utd were locked at 1-1 when the gathering gloom brought proceedings to a halt and a replay at Grassington, which took place last night.
Jeremy Gee had given Grassington the lead, only for Cononley to draw level with a Lee Thompson penalty.
Rimington Reserves retained the Norman Pratt Trophy for a fourth successive year when they defeated Settle United Reserves 4-0.
On a wet and windy night, Settle had early chances but could not take advantage of the elements, and Rimington scored two quick goals after the break.
Although Settle were denied a penalty, Rimington made the game safe with two further goals. Their scorers were Czpowski, Ratcliffe, Leach and Conti.