However, they encountered few problems as they won by 99 runs. After posting 185-8, with Mick Taylor making 45 not out, they brushed the Bronte men aside for just 86, with the wickets shared.
Wilsden entertained Bingley Congs and went down by 39 runs. Chris Mitchell (4-46) and Ben Reynard (4-42) helped the Beckfoot Lane side back to the hut for 115 before Matt Roberts (6-22) restricted the Windy Grove side to 76.
The West Craveners were dismissed for 138, with Kevin Pollard (36), Mark Paxton (25no) and David Scothern (21) being the main contributors as Harry McEneaney took 3-26.
The latter followed this with 27 and Joe Metcalfe made 22 in the hosts' total of 94, with Shane Taylforth claiming 4-16.
The hosts went first and battled their way to 147-8. Charlie Hassan (44) and skipper Graham Rishton (23) were the main contributors as Phil Binner (2-20) was the best bowler.
The Shires Laners were always on the back foot in reply, and when the score reached 106-7 at the end of the 31st over it was game on. Stephen Speak (24no) and Billy Winterburn (19no) took them to the next round with an unbeaten partnership of 43. Hassan (3-33) bowled very tidily.
Third-round draw: Ingrow St John’s v Crossflatts, Embsay v Thornton, Oakworth v Foulridge or Sutton (playing June 8), Haworth Road v Bingley Congs. Matches to be played on Sunday, June 15.