The opener’s 104 not out came from just 108 deliveries and included 15 fours, while Charlie Swallow (39 not out) provided some useful support at the other end.
Earlier, Toby Jacklin took a couple of wickets during the Ilkley innings, continuing his impressive start to the season.
Saturday’s result lifts Collingham up to fourth in the top-flight standings, where they sit six places above Beckwithshaw, who lost by 37 runs at Addingham.
George Stephens snapped up 3-17 as the hosts posted 245/6 in 50 overs.
Hector Hamill (47), Ben Holderness (37) and Sam Moore (36) all made useful contributions to Shaw’s run-chase, though they eventually ended up some way short of where they needed to be on 219.
Bilton are one position worse off and in the relegation zone following a 50-run defeat on the road at Horsforth Hall Park.
Jacques Allen (3-34) was the pick of the away attack, doing his bit to ensure that the home team did not progress any further than 191/7.
And although Jamie Bryan (43) and Cameron Martin (37) made sure that Bilton’s response got off to a decent start, they collapsed from 90/2 to 141 all out.
Follifoot remain third in the Division Two standings after romping to a comprehensive success at Green Lane.
Hector Bowerman, Istikhar Hussain and Josh Cutts claimed a couple of scalps apiece during the hosts’ first innings of 197/9.
The Bulls never looked in any real trouble as they set about knocking off the required runs and they went on to finish the job with seven wickets in hand and more than 14 overs to spare.
Tom Stewart (57) and Yasar Ali (53 not out) both struck half-centuries, while Bowerman (39) and captain Nick Robinson (34 not out) also batted well.
An excellent knock of 82 by Tom Franklin was not sufficient to save Bardsey from a 20-run reverse at the hands of Olicanian.
Tom Clayton’s troops were set 231 for victory, Waqas Rasheed(3-60) and Amjad Ali (3-73) visitors’ best-performing bowlers.
But, although Franklin was in good touch, he received little by way of support from his team-mates and Bardsey were knocked over with just 210 to their name.