Tyersal’s bid for a last-four place in the West Riding County FA Challenge Cup was thwarted by Rimington.
The East Lancashire League side were within minutes of losing 4-2 at the end of normal time but bounced back to level before snatching a 6-4 victory with two late goals in extra time.
Andrew Bailey (2), Glynne Beale and Martyn Glen scored for Tyersal, while Craig Sargeson (2), Robert Lloyd, James Tootal, Glen Dinsdale and a Sean Jackson own goal were on target for Rimington.
Bay Athletic, also from the West Riding County Amateur League, did make the semi-final stages, however, with a 2-1 win over West Yorkshire League Division One side Robin Hood Athletic.
Kieran Ryan and Danny Steele scored for Bay, with Dave Pickering replying for the visitors.
Campion Reserves lost their delayed West Riding County FA Challenge Trophy tie at home to Oxenhope Recreation Reserves 3-0, with Tom Thompson netting all of the goals.
West Riding County Amateur League Premier Division leaders Steeton took full advantage of Bay Athletic being on County Cup duty to strengthen their place at the summit with a 2-0 win at Marsden, with Sam Rooke and Damian Whiteoak scoring.
Salts moved up to second after beating last season's champions Ovenden West Riding 3-2, Kyle Berry, Joe Pleasance and Chris McTigue netting for the winners, Mat Devlin and Steve Senior replying for the Halifax side.
Littletown eased their relegation fears with a 3-2 home win over fellow strugglers Kirkburton.
Joe Jagger (2) and Lamin Bojang were the marksmen for the Beck Lane side, who were 1-0 down at half-time.
Goals from Joel Farrar, Craig Gilroy and Dale Wright gave Hunsworth a 3-0 home win over second-placed AFC Emley, denying the Huddersfield side the opportunity to take over top spot in Division One.
Wibsey moved out of the relegation places after drawing 0-0 with bottom-placed Storthes Hall Reserves.
Dudley Hill Rangers booked their place in the last four of the Division Two Cup, Roman Zurek (3) and Ryan Starr scoring in their 4-1 win over Steeton Reserves.
West Horton, who are a round behind, made sure of their quarter-final place with a 2-1 victory at Kirkburton Reserves.