Batley Bulldogs are 80 minutes away from a first Wembley trip with a golden point win against York in the 1895 Cup.
French half Louis Jouffret stuck a drop goal to settle a 17-16 victory for the Bulldogs at Bootham Crescent.
Martyn Ridyard had a similar impact for Leigh against Barrow at St Helens’ Langtree Park, as his one-pointer secured a 19-18 win and a semis spot.
They are joined in the last four by Sheffield and Widnes, with ties to be played on Sunday, 28 July.
The Wembley final takes place as a double-header with the Challenge Cup final on Saturday, 24 August.
Eagles won a South Yorkshire derby against Doncaster 32-28 at Featherstone, having come from behind late on.
Widnes, who were frequent visitors to Wembley in the Challenge Cup during the 1970s and 1980s in particular, hammered Dewsbury 54-6 to continue their progress.