It put Birstall level on points with title rivals Wrenthorpe whose game against lowly Batley was abandoned.
John Carruthers snapped up 4-44 as Ossett were restricted to 93-6 in a 25-over game.
Mark Atkinson (23no) and Chris Smith (22) led Osse
tt's scoring.
Indian opener Connor Williams (44no) put on 37 with Rob McFarlane (20) and shared an unbroken 49-run stand with Paul Marlow (21no) as Birstall knocked off the runs with more than eight overs to spare.
Birstall visit bottom side Scholes and Wrenthorpe travel to third-placed Methley in next Saturday's final matches.
Methley's title hopes ended when they lost by eight wickets to derby rivals Townville in a 40-over match.
Openers Tim Walton (57) and Stewart Clifton (55) shared an 87-run partnership and Peter Hepworth struck on unbeaten 31 as Townville comfortably overhauled 156-8.
Ryan Bradshaw and Chris Kippax each hit 52 as Methley recovered from 65-6. John Rickers was Townville's best bowler with 4-54 from 14 overs.
Wakefield Thornes' hopes of pipping Townville for fourth place in their first season in the top-flight were dented when they lost to Mirfield Parish Cavaliers.
Alex Scholefield (7-60) bowled out Thornes for 114 in a 35-over over match.
In reply, Ashley Mackereth struck 35 as Parish Cavaliers scraped a four-wicket victory with three balls left.
Stanley are poised to lift the First Division championship, needing just one point from their final game at Wakefield St Michael's to be certain of finishing top.
They are six points ahead of Altofts who visit Hunslet Nelson next Saturday.
Altofts have more six-point victories than Stanley, a deciding factor if they finish tied on points.
Gildersome clinched the Second Division championship with an eight-wicket win at Batley who were skittled for 67.
Alan Wailes's 9-48 was in vain for second-placed Methley in a 76-run defeat at Townville.
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