Ben Holderness' men looked dead and buried at the halfway stage of Saturday's Airedale & Wharfedale League Division One clash after Redmond Bolton's sensational knock of 186 from just 103 deliveries saw their free-scoring hosts post 405/9 from their 50 overs.
But, 'Shaw made a decent fist of what seemed a near-impossible run-chase, batting with real urgency to keep themselves just about in the contest.
Alex Morrell (55), John Inglis (52), Miles Buller (51), skipper Holderness (51), Ross Sedgley (44) and Callum Doak (38) all contributed, with the majority of them scoring at quicker than a run-a-ball.
In the end, the visitors would however finish up 44 runs short on 361/9, slipping to their third defeat in as many games this season.
Bilton are in the same position as Beckwithshaw and still searching for a first win of the campaign, having gone down by five wickets on the road at Saltaire.
David Hardcastle top-scored with 34 in a well below-par score of 123 all out, one which never looked like being enough against the defending champions.
And Saltaire knocked off the required runs with relative ease, making it to 127/5 inside 31 overs.
Collingham & Linton began 2022 with back-to-back victories but were also beaten on Saturday.
Having slumped to 99/6 away at North Leeds, valuable lower-order runs from Jack Burke (59) and Toby Jacklin (54) guided Jonathan Haslem's team to a competitive total of 234 all out.
The in-form Jacklin then completed a superb afternoon's work by taking four wickets when the hosts replied, but that wasn't enough to prevent the Leeds outfit from completing a five-wicket success in the 43rd over.
In Division Two, Follifoot's bright start to the season was also brought to an end as they suffered a 66-run reverse at home to Pool.
Istikhar Hussain (3-65) and Yasar Ali (3-91) each took a trio of scalps at some cost, the visitors eventually closing on 255/8.
The Bulls looked to be out of the contest when they slumped to 108/7 in response, though a rapid innings of 63 by Hussain offered a glimmer of hope.
His dismissal did however leave Follifoot well short of where they needed to be on 189.
Bardsey did however get off the mark for the year courtesy of a three-wicket win at Green Lane.
Waqas Rahseed (3-56) was the pick of the visitors' attack, helping to ensure that the home team did not progress any further than 184/9.
Mohammed Altaf (43) and Sameer Manjrekar (41) then came together to set Bardsey on their way to a routine triumph.