Thornhill Trojans booked a place in the third round of the Challenge Cup after an impressive 38-20 win over Russian side Strela Kazan on Saturday.
St Helens are the reigning Challenge Cup champions
The Dewsbury club reached the fourth round last year before losing to Super League side Catalans Dragons.
Meanwhile, Normanton Knights sunk the Royal Navy's dreams of Cup success with a narrow 28-26 win.
Saddleworth Rangers secured a 21-14 win over Siddal, while Drighlington beat Wigan St Jude's 30-22.
Leeds Metropolitan University, shock winners over Wigan St Patrick's in the first round, went out with a 34-18 defeat at Premier Division leaders Leigh Miners Rangers.
Two ties were postponed: Hull Dockers v Eastmoor Dragons and Seaton Rangers v West Bowling.
The Carnegie Challenge Cup Third Round Draw will be staged at 1715 GMT on Sunday on BBC Radio Leeds.
The sides to make it through the second round will join 22 professional clubs from the National League together with three French clubs, Limoux, Pia and Toulouse and one more Russian club Lokomotiv Moscow.
Super League clubs enter the competition at the fourth round stage.
Challenge Cup second-round results:
West Hull 23-16 Skirlaugh
Eccles and Salford Juniors 40-28 Egremont
Leigh Miners Rangers 34-18 Leeds Met University
East Hull 50-4 Dewsbury Celtic
Royal Navy 26-28 Normanton
Hull Dockers P-P Eastmoor
Rochdale Mayfield 50-0 East Leeds
Widnes St Maries 22-6 Hull Isberg
Saddleworth 21-14 Siddal
Thornhill 38-20 Strela Kazan
Bradford Dudley Hill 26-28 AET Castleford Lock Lane
Leigh East 10-25 Oulton
Seaton P-P West Bowling
Wigan St Judes 22-30 Drighlington