Ouseburn hold an 18-point advantage over Birstwith and require one more win in their four remaining matches to raise the trophy.
Sam Parker smashed an impressive century and shared a 160-run partnership with captain David Cummings (95) as Ouseburn scored an unreachable 289-4 on Saturday.
Parker hit 13 boundaries and a six in his 111 not out, which saw him also put on 61 with fellow opener Adam Fisher (24) and 66 with Jamie Bryant (45).
In a rain-reduced fixture, Hampsthwaite gave a strong account of their batting skills and totalled 202-3 from 38 overs.
Leeds United's new predicted Premier League finish after big change and alarming slide of rivals
What Leeds United said on outstanding Raphinha payment as Barcelona make another drastic move
Leeds United braced for disappointment as transfer rival reportedly agree £21 million deal
Leeds United transfer news: Leeds ‘set aside club-record fee’ for striker deal, Southampton ‘willing’ to sell Whites target
Leeds United news: PSG make Arnaud Kalimuendo decision as former Whites man expresses Joel Robles 'surprise'
Captain Sam Dabin remained unbeaten on 84, while opener James Cousen hit 48.
Birstwith’s title chances were washed down the drain in a 78-run loss at Helperby.
Reduced to 41 overs per side, Helperby amassed 200-7 with Trevor Chibvongodze (72) and Luis Rees-Hughes (60) compiling the early impetus.
Batting has been Birstwith’s strength in the 2016 summer but they struggled against the Helperby attack of Dan Marston (3-37), Joe Corner (2-33) and Matt Cavanagh (2-22).
The challenge of long-term pursuers Darley came to a crashing halt at neighbours Pateley Bridge after they were bowled out for 139, the hosts sealing a four-wicket win.