Ryan Bradshaw's men followed up their earlier victory back in May with a strong batting display, posting 262/8 from their 50 overs having won the toss.
Siraj Hussain led the way, hitting 73, while skipper Bradshaw (37) and opener Cameron Martin (35) also contributed.
Oliver and Peter Hotchkiss did their best with the ball for 'Shaw, both finishing up with three wickets to their name.
The visitors got off to a decent start in reply and made it to 75 for the loss of just one wicket, Dax Guy (34) and Sam Moore (24) doing their bit.
Mustahsan Ali Shah then took the game by the scruff of the neck, getting rid of six 'Shaw batsmen with a fine spell of bowling.
Ross Sedgley (30 not out) offered some resistance, but eventually ran out of partners as last season's champions were dismissed for 177.
Defeat leaves relegation-threatened 'Shaw 34 points adrift of safety, while Bilton remain ninth, just behind Follifoot in the league standings.
Alex Fox's team suffered a six-wicket reverse at the hands of Pool on Saturday having been dismissed for 167.
Matthew Williams struck 54 and Yasar Ali 31, but the hosts' total never looked like being sufficient.
Pool didn't have things all their own way when they took their turn at the crease, and Istikhar Hussain did claim a couple of scalps, but the visiting side eventually finished the job in the 41st over.
Collingham & Linton pulled 18 points clear at the top of Division Two after a comprehensive win at Colton Institute.
Nishant Desai smacked 13 fours and two sixes in a rapid 49-ball knock of 90, while Charlie Swallow (73 not out) and Jonny Haslem (56) also registered half-centuries for the league leaders.
The trio's efforts left Collingham in a strong enough to position to declare on 278/6 after 49 overs and their hosts never looked like getting anywhere near their victory target.
They slumped to 30/4 early on, and although they rallied briefly, Chris Bridge (5-36) and Steve James (4-39) performed superbly with the ball to ensure that the home reply didn't get any further than 131.
Third division Bardsey are another side leading the way in their respective league.
Runs from Naseem Aslam (63) steered them to 237/7 on the road at Shadwell before Sameer Manjrekar (4-28) and Amjad Ali (3-43) helped get rid of the hosts with only 139 to their name.