Liphook won the toss and bowled first and made scoring difficult for the home side in cloudy conditions, with only 40 on the board by the 18th over, although taking wickets proved elusive.
Suman Ganguly made the breakthrough, and when Ric Williams ran out opener Thomas Hockenhull for 40 the hosts were on 88-3.
Rhys Oxley scored 50 in as many deliveries, providing some much-needed momentum for Fair Oak as they scored 190-9 off 50 overs.
Only Ganguly (4-29) provided a real threat, although George Neave (2-39) and Chaz Janzcur (2-41) took two wickets each.
Liphook were soon rocked back on their heals as opening spinner Charlie Gwynn (4-14) dismissed Rob Nicklin and Harry Munt.
When Ganguly was caught by Gwynn for 25, it was left to an exemplary patient 46 from opening batsman Chris Martin to keep the ship afloat.
When Martin finally fell in the 40th over, Liphook were very much in trouble at 112-7.
It was left to a spirited tail end effort led by skipper Sean Burton (15), Daniel Harvey (20) and Janczur (21 not out) to provide a late assault on the Fair Oak total.
Burton, Harvey and Janczur’s running between the wickets was key.
With just three balls to spare, it took a run out of number 11 Dave Elliott by Gwynn to end the Liphook innings at 185.