In a game reduced to 33 overs a side due to rain, the visitors posted 190-5, opener Chris Till smacking nine fours and two sixes in a strong 78 from 78 balls.
David Snowball (3-53) and Charlie Hopper (2-34) were the pick of the home bowlers.
The home side lost two early wickets and were struggling at 13-2 when Adam Eustace departed for seven and Tom Bussey for a duck.
The experience Nick Zakrzewskit (24) helped put on 49 for the third wicket with skipper Cowell, but when the former was dismissed and Josh Mainprize for three, the home side were again in trouble at 79-4.
Youngster Brad Milburn (17) then shared a sixth-wicket partnership of 71 with Cowell as the home side looked to fight back for a dramatic win, but after Milburn's departure the skipper followed for an excellent 114 from 107 balls including nine fours and seven sixes and the hosts ended their run-chase agonisingly short on 181-6.
Rain put pay to the York Premier League North game between Scarborough and York, the latter making 24-0 in the five overs possible before the heavens opened.
No play was possible either in Folkton & Flixton's Premier Division game at Whitkirk.