Addingham managed to escape most of the bad weather but they could not prise out the final Bardsey wicket which would have given them victory.
In a rain affected game Addingham perhaps batted too long in taking their full 50 overs.
They finished on 204-8 with Darrell Robinson making an unbeaten 52 and skipper Chris Taylor 31. This was after Australian opener Toby Stapledon had made 35.
Bardsey's Nick Ryder bagged a return of 6-76 off his 25 over stint.
Bardsey were then teetering on the brink of defeat at 138-9 when their 31 over innings ended.
Their opener Danny Wilson had held their innings together with a gutsy innings of 84 as Chris Taylor (3-45) and Simon Farrand (3-41) tried to force victory with the aid of Chris D'Arcy (2-28) and Chris Campbell (1-9).
Horsforth took the opportunity to steal a march on their title rivals Bardsey by gaining an eight wicket win over Olicanians.
Horsforth's opening pair Ben Clarke and Chris Binks shared a crucial stand of 78 which came off just ten overs as they pushed their side past the Ilkley club's total of 92-6 made in 29 overs.
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