Their immediate reward is a home tie against Doncaster provisionally arranged for next Sunday.
Chorley also defeated St Annes on Saturday in a thrillingly close finish to the Vaux Bitter Cup first round match at Windsor Park to earn a bye into the semi final and a home tie versus either Darwen or Blackpool.
Darwen enjoyed a comfortable victory at home to Morecambe, professional Peter Sleep hitting 94 and fellow opener Nigel Robbins scoring 72 in a total of 218-2 from their 40 overs.
Morecambe slumped to 95-9, Andy Mercer taking a magnificent 5-18 from eight overs.
Delighted Chorley skipper Roland Horridge said: ``It has been a fantastic weekend for the club and to be in the quarter finals of the national club championship yet again is a tremendous record. ``Our bowling and fielding in difficult conditions against Birkenhead Park was quite magnificent.''
Horridge himself led by example, producing vital knocks in both games. After Birkenhead Park had been pinned down throughout their 45 overs by tight bowling with Nigel Heaton claiming 4-25, Chorley were left with a modest target of 139.
But they lost three wickets for 38 before Horridge (43) and Neil Senior (46) rebuilt the innings with a crucial partnership of 92 for the fifth wicket. Both were out within 10 runs of victory as Chorley reached 139-5 with nine overs to spare.
Saturday's match went right to the wire before Chorley edged home with just one ball of the last over remaining.
Eldine Baptiste led the way with 64 as St Annes posted a challenging 184-7 and Chorley left themselves needing brisk acceleration in the last ten overs to bring the target within reach.
Horridge (39) and Nigel Heaton (38) provided it and with five needed from the final over Michael Critchley saw his side to a five wickets victory by coolly straight driving Baptiste for two fours.