Addingham have had a miserable start to the season, lying second from the bottom of Division Three with only one league victory to their name.
And even though Rawdon have not exactly set Division One alight, they have the league scalps of Steeton and Bilton and were expected to get through this one comfortably.
So it looked when Andrew Doidge picked up three quick wickets to reduce Addingham to 81-5 — but Calvin Hewitt (77no) and Henry Barrow (33) put on 95 for the sixth wicket and the visitors finished with a respectable 198-8.
A rain break reduced the target to 133 but even then Rawdon just could not get going.
Ricky Palacio (3-30) dismissed three of their top four batsmen and ran out James Doidge, before Tom Smallwood (3-23) finished things off.
In the record books it will say a 13-run win but it was more decisive than that and it booked Addingham a visit to Adel in the next round.
Ryan Sharrocks and Mahir Ali picked up three wickets each as Pool were dismissed for 118. Ollie Hardaker, who hit 36 in 31 balls, and Bailey Worcester (29no) then clinched a home tie against league leaders Otley, who comfortably overcame Menston by 116 runs.
Rain reduced Kirkstall’s 166-7 to a target of 131 and Harrison Durkin (65) made sure Guiseley went through to the next round, where they will face Bilton.