David Cummings' men beat New Rover by one wicket on Saturday afternoon, reaching their victory target off the final ball of the match.
The visitors had got themselves into a strong position by the halfway stage of the contest, posting 259/8 from their 50 overs despite the efforts of Luke Jarvis (4-66).
But Jacques Allen got the Bilton reply off to an excellent start, the opening batsman hitting 12 fours and one six on his way to an impressive score of 108.
Chris Peirson (48) and Ryan Bradshaw (41) kept the home team ticking over, and although the game went right down to the wire, they eventually made it over the line at the death.
Victory lifts Bilton out of the bottom two and up to eighth position in the table.
They now sit two places and three points better off than Beckwithshaw, who suffered a comprehensive defeat at Rawdon.
George Stephens took four scalps, though the hosts were able to make their way to 281/8 having won the toss and elected to bat first.
Oliver Hotchkiss (74) and John Inglis (40) both looked in decent touch during Shaw's response, however they were all out for 194 in the end.
Collingham & Linton remain fourth after routing Addingham to record their fifth success in eight attempts this term.
The in-form Charlie Swallow followed up last week's ton with another fine knock, weighing in with 59 of the home side's 216/9.
Toby Jacklin added 31 and then went on to complete a superb afternoon's work by bagging 7-25 to help send Addingham on their way with only 101 to their name.
Follifoot took over at the top of Division Two courtesy of a 99-run triumph at home to Calverley St Wilfrids.
Skipper Nick Robinson led by example, plundering 21 fours and four sixes in a superb innings of 143 not out which came from just 130 deliveries.
Nat Cutts also played his part with the willow in hand, adding a rapid 65 as the Bulls posted 285/7.
Cutts then showcased his all-round talents by scooping 4-39 when St Wilfrids took their turn at their crease, ably assisted by Istikhar Hussain (3-33).
The pair's efforts went a long way to ensuring that the visitors did not progress any further than 186, leaving them well short of where they needed to be.
Amjad Ali (5-26) and Waqas Rasheed (4-45) combined to great effect as Bardsey knocked Harden over for 111.
Tom Clayton's troops made hard work of knocking off the required runs, slumping to 52/6 at one stage, but they got the job done eventually thanks largely to Sadaqat Zaman's innings of 39.
Saturday's win lifts Bardsey up to fifth spot in the second-division standings.