Havant will be at home to Reading in the Cockspur Cup south region final on Sunday, July 2.
They caned Bournemouth by 103 runs after Andy Perry (116) and Ben Walker (57) led the way towards a massive 256-5 in 45 overs.
Academy off-spinner Stuart Ransley took 4-14 as Bournemouth were dismissed for 153 (Dan Jarman 34). Another Hants Academy starlet, Benny Howell, hit 99 as Reading made 261-8 before skittling Finchampstead for 119.
Cockspur Cup fifth round draw includes: Frocester or Bristol West Indians v Bath, St Just v Taunton St Andrews, Havant v Reading, Oxford v Ealing, Brentwood or Chingford v Brondesbury, Blackheath v Wanstead, Teddington v Brighton & Hove, Horsham v Bromley.
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