Ben Holderness’ men recorded what was a first win in five attempts having racked up a sizeable total of 338/7 from their 50 overs.
Miles Buller (88) led the way with a quick-fire half-century, though he was not alone in performing well with the willow in hand.
Ross Sedgley (72), Oliver Hotchkiss (49), skipper Holderness (31) and Peter Hotchkiss (26 not out) also did their bit to leave Shaw in full control of proceedings.
Not to be outdone, the home bowlers also excelled as North Leeds were knocked over for just 105, Oliver Hebblethwaite in seriously impressive form as he bagged 7-45 alongside Joe Holderness (2-39).
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Saturday’s result elevates Beckwithshaw to ninth in the table, where they now sit just three points behind local rivals Bilton.
David Cummings’ team were left with it all to do by Otley as they attempted to chase down a first-innings score of 296 all out.
Cummings himself had produced an absolutely incredible bowling performance, taking a sensational haul of 9-59 after losing the toss.
He then completed a fine afternoon’s work by making 51 not out, however the away response was ended by the rain at 103/5 in the 25th over, with the Duckworth-Lewis method condemning them to defeat.
Collingham & Linton remain in fourth position despite suffering their second defeat on the bounce when they travelled to Rawdon.
Charlie Swallow (96) narrowly missed out on a ton, while Daniel Kilby (53) was also in good touch, helping the visitors to 249/7 from their 50 overs.
Rain meant that only 38 overs were possible when Rawdon replied, and they reached their revised target of 198 with ease, closing on 201/3 despite a couple of early wickets for all-round ace Swallow.
Follifoot sit second in Division Two following a six-wicket success at Colton Institute.
Alex Fox took four scalps, but couldn’t prevent the hosts putting a more-than-useful 291/7 on the board.
The wet weather saw the Bulls left needing a revised target of 247 for victory in 39 overs and they did not hang about.
Nat Cutts smashed a rapid 134 not out from only 100 balls, a knock which included 15 fours and two sixes.
He received support from Hector Bowerman (32) and Yasar Ali (31) as the visitors made it over the line with two-and-a-half overs to spare.
Sixth-placed Bardsey came up agonisingly short away at Adel.
Amjad Ali knocked over five home batsmen as the hosts were dismissed on 263.
A slight rain delay left the away team chasing a revised score of 260 in 49 overs and they got off to a near-perfect start.
Sameer Manjrekar (95) and Naseem Aslam (93) put on 176 for the first wicket, and although Eddie Clayton added 34, Bardsey ended up missing out by one run as they ran out of deliveries on 258/6.