Darwen set a formidable total of 189 from their 40 overs thanks to a fine opening stand of 120 between Sleep and Nigel Robbins (42).
The phenomenal Darwen pro took complete control in front of the Birch Hall side's largest crowd of the season.
Blackpool's reply began well as they progressed to 57 without few alarms but the introduction of Paul Rodden and Neil Cordingley into the attack had a devastating effect.
Each took four wickets as the Seasiders lost 10 wickets for only 28 runs to give Darwen their third victory in four games by a margin of over 100 runs and a visit to Chorley in the semi-final.
On Saturday Darwen's fixture at St Annes was abandoned with the game delicately poised following a freak thunderstorm.
St Annes had posted a total of 219 against a weakened Darwen attack missing their regular bowlers with Darlington reaching a century on the last ball and professional Baptise dropped early on hitting 70.
Darwen lost early wickets, but when the rain came they required 105 from 22 overs with Gareth Cordingley still there on 46 and their victory push was thwarted.
It was a weekend of misery for Chorley. A second consecutive defeat blew a hole in Chorley's title hopes at Windsor Park on Saturday. They must have expected another maximum points haul against Blackpool, a side they had already defeated comfortably in two cups this season.
But the home side never recovered from an early collapse which saw them reduced to 11-3, and they failed to reach a challenging enough total despite a gallant fightback led by Gary Mayor and completed by a battling half century from Mark Richardson.
A solid partnership between Rob Bracewell and Gavin Wiggins helped Blackpool home, though home debutant Iqbal Patel did give the Chorley supporters some cheer with a lively spell which brought him two wickets.
The dream of a return to Lord's ended on Sunday as Chorley crashed to defeat against Doncaster Town in the Abbot Ale Trophy quarter final. And for the second time in two days, it was a dreadful start which cost Chorley dear.
A devastating start by Doncaster paceman Graham Attenborough had them reeling at 11-4, and though skipper Roland Horridge and Gary Mayor led a gritty revival, the final total of 129 never looked enough, Doncaster edging home in the penultimate over.