Walker was in superb form with bat and ball as he first hammered an unbeaten 98 from just 69 balls in a big hitting innings which included six sixes and nine fours.
He was supported by another fine knock from in-form overseas player Tayyab Tahir, whose innings of 63 took his tally for the season to 668 runs, while opener Nick Lindley made 37 which helped Cleckheaton post an impressive total of 274-6.
Walker followed up his efforts with the bat by taking 4-51 and with support from John Wood (3-40), St Lawrence were dismissed for 193.
James Smith (44), Charlie Best (33) and Mark Robertshaw (33) all made good starts but were unable to go on and produce match winning innings.
Cleckheaton have now registered back-to-back wins over the top two and have moved into eighth place, pulling well clear of the danger zone.
Their latest success also allowed Farsley to leapfrog St Lawrence to move second following a six-wicket win over Townville.
The visitors chose to bat first but were bowled out for 126 as spinner James Logan returned impressive figures of 6-12, while opener Jonathan Booth (36) was the only batsman to make an impression.
Farsley lost four wickets as Harry Clewett claimed 3-19 but reached their target thanks to Dan Hodgson, who played a key role of 39 not out, to steer his side home and they are now just nine points off the top.
Fifth-placed Methley are just 25 points behind leaders New Farnley after being made to work hard for their 13-run win over Lightcliffe.
Opener Marcus Walmsley (50), Adam Patel (40) and Grant Soames (37) helped Methley to post a challenging total of 245-8.
Lightcliffe looked as if they might chase down the home-side’s score until opener Alex Stead was run out for 73.
Jonathan Wilson (46no) and Suleman Khan (33) couldn’t quite maintain the required rate as their side finished on 232-6.
Lightcliffe are 23 points clear of second-bottom Bradford and Bingley, who they face this Saturday.