Whitestar, who have won just one league game so far this season, drew 3-3 with the current Premier Division leaders before holding their nerve to win 4-3 on spot-kicks at Sandylands.
Whitestar keeper Andrew Shutt saved several one-on-one chances and then two penalties.
After going ahead through Daniel Cox, Silsden came under immense pressure and Luke Howson levelled for LMS before the break.
Jamie Cunningham hit a screamer for Silsden on the hour-mark but Howson popped up again to take the tie into extra time.
Skipton continued to batter Whitestar’s goal, but Shutt was colossal. Oliver Hurst finally put LMS in front before Cox took the game into penalties with the last kick of the game and Whitestar held their nerve.
Oxenhope went down 7-4 against Premier Division Grassington, who are three divisions above them.
With the top flight side’s pitch unavailable, the tie was switched to Rec’s slope and the hosts took advantage when Shaun Humphreys put them in front.
Grassington hit back with two goals, before Sam Coates and Humphreys restored home advantage, only for the visitors to respond.
As the second half progressed Grassington’s young legs proved the deciding factor as they notched another four before Rec man of the match Humphreys claimed his hat-trick.
Grassington’s scorers were Tom Bradford (2), James Morgan, Ben Schindler, Nicky Wright, Jan Ozdoba and an own goal.
Wilsden, the unbeaten leaders of Division One, went down 4-1 at home to Cononley Sports in the League Cup. Two goals from Chris Lumsden, plus strikes from Shane Green and Mark Bradley took Cononley into the last eight.
Earby Town needed extra time to defeat AFC Colne 3-2 in the Division Two League Cup. Martin Bowker’s double and a goal from Ashley Garbutt saw them into the next round where they will be joined by Silsden Whitestar Reserves who beat Skipton Town 2-1.
Gavin Shearer and Ben McClennon were on target for Whitestar while substitute Bill Knight replied.
Sutton switched their Division Three League Cup tie to the ground of opponents Settle United Reserves and emerged with a 4-3 win.
Joshua Smith’s two goals were added to by strikes form John Crummack and James MacDonald. Settle replied through Ian Wildman (2) and Daniel Lambert.
Aaran Abbas netted twice as FC Sporting Keighley won 3-1 at Bradley Reserves in the Division Four League Cup. Munzir Nazir was also on target for Sporting while Jack Maude replied for Bradley.
Crosshills moved to within three points of Division Three leaders Cononley Sports Reserves with a 4-2 win over Ingrow & Worth Valley.
Two goals from David Harrison took Ingrow into a 2-1 lead, but Cross Hills took the points with two long-range strikes from Ben Dewhirst after Billy Skelton and Adam Greenwood had scored the first two goals.
Carl Drewett (2) and Craig Quigley were on target as Grassington Reserves won 3-1 at Cowling Reserves.
Addingham ran out comfortable 4-1 winners over Sutton Reserves in Division Four thanks to two goals from Tom Bancroft and one each from Don Jordan and Jake Parkinson.
Skipton Town defeated Horton by the same score with Jonathan Nash scoring twice.