Mally Nicholson made 74 and opener Andy Gorrod 71 as Cleckheaton posted a challenging 245-6, while Richard Whitehurst struck three sixes in the final over, bowled by off-spinner Steve Watts, which proved to be crucial in the outcome of the match.
St Lawrence made a strong bid to reach their target with the league’s top run-scorer, opener Mark Robertshaw, leading the way with 97.
This took his tally for the season to 631, helping the visitors to make 231-9, which gained them maximum batting points, but not enough to win.
Overseas leg-spinner Tanzeel Altaf (5-56) and paceman Iain Wardlaw (3-76) were Cleckheaton’s most successful bowlers.
Second-placed Woodlands kept in touch with the leaders ahead of next Saturday’s match between the top two with a 55-run win at Lightcliffe.
Logan Weston was top-scorer with 57 not out ,while opener Sam Frankland made 44 and Sarfraz Ahmed 31 as Woodlands reached 222-6, three short of a fifth batting point.
Overseas player Suleman Khan hit 46, but received insufficient support as Lightcliffe settled on 167-8, with Scott Richardson taking 4-42.
Mark Harrison’s winning start as Farsley’s captain continued as they beat Morley by two wickets.
Harrison, who took over as skipper a fortnight ago, led his side to victory over Pudsey Congs in his first match in charge and led from the front in this match, top-scoring with 55 as fourth-placed Farsley eased past Morley’s 153-9 with five overs to spare.
Morley were in deep trouble at 58-8 until second-team player Richard Winn scored an unbeaten 70. South African Graham Hume achieved his fourth five-wicket haul of the season for Farsley, taking 5-19, while Neil Laidlaw took 3-32.
Pudsey Congs lifted themselves off the foot of the table with a tense one run win over fellow strugglers East Bierley.
Bierley needed two runs from the last ball to win the game, but Luke Jarvis was run out to leave Congs the winners by the narrowest of margins.
Andrew Bairstow (41) and Barbar Butt (34) were the top scorers as Congs made 195-8. Nicky Rushworth (52) and Gavin Hamilton (45) led the way for Bierley, but they fell one run short on 194, with opening bowler Mubtada Akhtar taking 4-56.
John Carruthers claimed his 1,000th Bradford League wicket during his spell of 3-28, while new-ball partner Dan Busfield took 3-18 as Yeadon were bowled out for 73, despite the loss of seven overs in their innings.
Earlier, Hanging Heaton had made 181-7, with former Yeadon batsman Ben Elvidge top-scoring with 47 and Nick Connolly making 42. Muhammed Saeed was Yeadon’s best bowler with 5-53.