While Cumbria were scrambling a last ball/last wicket win in Herefordshire their group rivals Northumberland had more in hand beating Lincolnshire.
The other game in Group One saw Northumberland beat Lincolnshire by six wickets at Scunthorpe.
Former Leicestershire opener Sam Evans carried his bat for 113 for Lincolnshire and shared a fifth wicket stand of 107 with Jordan Cook (56).
But the last five wickets went down for 32 and Northumberland paced their chase to perfection.
Coach Dan Shurben led by example with 41 and he shared a second wicket partnership of 107 with Ross Whitfield.
Whitfield (83) and Ben Robinson (63 not out) then got Northumberland most of their way to a target of 237 which they reached with 11 overs in hand.
Oxfordshire were the spare team on the first day and they open their account against Cumbria on Sunday at Kendal.
Cumbria will follow up at Allendale CC on Sunday, June 18 against Northumberland and will play Lincolnshire at Keswick on Sunday, June 25.
Hoping to get through the group again as one of the top two Cumbria would have a quarter final on Sunday, July 2.
The semi-final is set for Sunday July 16 (reserve day Monday July 17) and the final is on Sunday August 27 at Wormsley (reserve day Monday August 28).
Cumbria have been beaten by Berkshire in all of the last three trophy finals, and will have been surprised to hear that their conquerors have started this year’s campaign with a defeat – and a heavy one at that.
Berkshire, aiming to win the competition for a fourth successive season, were spun out for 107 by Hertfordshire slow left-armer Ben Waring, who took five for 21, and were beaten by 85 runs.
Only Charlie Dunnett and Euan Woods topped 20 in Berkshire’s innings with former Essex seamer Jack Plom playing a valuable supporting role to Waring with three for 33.
Earlier Dominic Chatfield made 60, the only half-century of the match, and shared an opening stand of 66 with James Latham.
David Burnell’s patient 33 also proved valuable against Berkshire’s four-pronged spin attack.
Other scores were:
Group Two
Truro: Cornwall 303-8 (Jack Paull 63, Paul Smith 60 not out, Will MacVicar 50), Devon 267 (Jack Thomas 70, Calum Haggett 60, Max Tryfonos 5-38). Cornwall won 36 runs.
Group Three
Mildenhall: Cheshire 236-9 (Henry Dobson 70, Ben Claydon 5-39), Suffolk155 (Nick Anderson 5-24). Cheshire won by 81 runs.
Group Four
Marlborough College: Buckinghamshire 240, Wiltshire 243-7 (Ed Young 75). Wiltshire won by three wickets.
