Saturday's Airedale & Wharfedale League Division One clash saw hosts 'Shaw win the toss and elect to bat first.
Ross Sedgley (36) and Ben Holderness (35) both made starts at the top of the order to set the Stags on their way before Sam Moore (53 not out) and Miles Buller (43) took over, helping lead their side to 234/6 after 50 overs.
Kieren Helwig and Toby Jacklin both took a couple of scalps for Collingham, though those wickets did not come particularly cheaply.
Daniel Kilby's fine century got the away response up and running, the opener hitting seven fours and three sixes in his 126-ball knock of 116.
Charlie Swallow then finished the job, scoring 59 not out as Collingham reached 235/4 in the penultimate over.
That result keeps them fourth in the table, while Beckwithshaw sit 10th, just one place above the relegation zone.
Bilton failed to build on what was a much-needed success over New Rover last time out, going down by 48 runs away at Addingham.
Luke Jarvis bagged 4-35 as the home team posted 198/9 from their 50 overs after being put into bat.
Sam Dale (53) struck a useful half-century when Bilton replied, though he received little by the way of meaningful support from his team-mates and the visitors failed to progress beyond 150/9.
In Division Two, Follifoot beat Olicanian in comprehensive fashion to consolidate their position at the top of the table.
The Bulls' batsmen laid the foundations for a seventh victory in nine attempts this season, captain Nick Robinson again leading by example.
His innings of 79 was added to by Istikhar Hussain (66), Yasar Ali (54) and Hector Bowerman (42) as the away side put a sizeable 293/9 on the board.
Olicanian's turn at the crease began well enough, though they struggled to keep up with the required run-rate.
And a trio of scalps apiece for Joshua Cutts and Ali helped ensure that they ended up well short, all out for 207 in the end.
Elsewhere in the second tier, seventh-placed Bardsey lost out by six wickets on the road at Steeton.
Tom Franklin (89) and Eddie Clayton (34) chipped in with important runs in a first-innings effort of 199 all out.
Amjad Ali got rid of three Steeton batsmen when the hosts replied, however he was unable to halt what would become a relatively straightforward cruise to 205/4.