With the scores tied at 16-16 at the break, the visitors produced a superb second-half performance to move into the final four, where they will face the University of Gloucestershire All Golds.
The All Golds progressed after recording a 36-28 win against Newcastle Thunder in their quarter-final clash.
With the match delicately poised at 10-10 at the break, the hosts took control in the early stages of the second half, with Jonny Leather and Phil Cowburn touching down to give Gloucestershire a healthy lead.
Ali Blair and Derrell Olpherts reduced the deficit for Newcastle, only for Steve Parry and Lewis Reece to extend the All Golds' lead. Vincent Rennie gave the visitors hope when he crossed, but Ollie Purslow put the result beyond doubt when he went over in the corner.
Meanwhile, Keighley will face London Skolars in the other semi-final after the Cougars cruised past Oxford on Sunday.
Paul White got the first try of the match before crossing again in the second half as Keighley beat their visitors 54-14.
The Skolars booked their spot in the last four thanks to a 24-12 win away at Doncaster.
Eddie Mbaraga touched down twice for the visitors, with Sam Nash and David Williams also getting on the scoresheet.
