Zulqernain Haider (50), Imran Dawood (59) and Azhar Chunara (38) all chipped in with useful runs as Liversedge closed on 223-6, with opening bowler Ben Burkill (3-53) the pick of the Scholes bowling.
Nahim Ashraf (74) and Craig Wood (40) produced a 104-run stand for the second wicket in reply before a collapse saw six wickets fall for 59 runs.
Ross Irving (30) did well in the middle order but Scholes ended 26 runs short as they were bowled out for 197 in the penultimate over.
Simon Kay claimed 3-38, while Dawood capped a fine game against his former club by taking 3-47.
Sunday's cup win capped a fine weekend for Liversedge, as they moved up to sixth place in the Central Yorkshire League Premier Division on Saturday after a 40-run home victory over Mirfield Parish Cavaliers.
Overseas man Haider was again in form with the bat, top scoring with 33.
Richard Soulsby (32), Danny Broadbent (27) and Simon Kay (26) also batted solidly as they totalled 186-6.
Anthony Bailey took 3-33, Will Atkin 2-26 and Mohammed Shahnawaz 2-57 for Parish.
After a stuttering start in reply, Alex Scholefield (41) and Iqbal Khan (31) offered Parish hope but once they were gone the innings fell away and they were dismissed for 146 as Kay took 2-9, Simon Purdy 3-50 and Jonny Gould 4-32.
Scholes are still aiming to break their duck in the league after a fourth defeat, by 109 runs at Ossett.
Nick Connolly (112) and Jamie Sadler (111) were in sparkling form as hosts Ossett made 259-3.
Burkhill again shone, taking 2-58.
Scholes's reply never gained any real impetus and after being 73-6 they were finally 150 all out.
Nahin Ashraf made 29 and Burkhill 28 as Chris Smith did most of the damage with 6-44.
Liversedge A were unable to produce a shock result in Sunday's Barry Winstanley Cup first round as they bowed out to Hunslet Nelson first team.
Liversedge suffered at the hands of Kashif Rashid as they were beaten by 151 runs.
Rashid blasted 118 and with support from Matt Smith (56), Nelson reached 243-8.
Steve Wright claimed 3-31 but although Mark Palmer (24) top scored in reply, Liversedge were bowled out for 92 as Sohail Raz claimed 4-17.
On Saturday, John Newsome made 27 and Jamie Hardcastle 24 as Liversedge A were held to 147-9 in their CYL Division Two clash at Methley A.
The home side then cruised to 150-2 in 28 overs as James Marston hit 54 not out.
Scholes A lead Division Three thanks to a 130-run win over Gildersome A.
Neil Kellett (50), Andrew Spencer (24) and Andrew Jackson (23) helped guide Scholes to 199-9 before Daniel Russon (4-17), Andrew Jackson (3-15) and Christian Jackson (2-19) saw the visitors shot out for just 69.