Leamington lost regular wickets after a combination of poor shot selections and poor umpiring decisions which meant that despite Zack Fagg (60 off 46 balls) getting the innings off to a flyer, no one else in the home side was able to follow up his early example.
Once Fagg departed, no one else really came to terms with the visiting attack as Howell (2-50) and Davenport (4-34) ensured that Leamington posted a sub-par score of 192.
Rob Williams (33) and Vidhyesh Balasubramaniam (21) were the only other scores of note.
In reply, the visitors got off to a positive start as captain Cox (59), Patel (35) and Ahmed (33*) ensured that there were no great alarms as Old Hill cantered to victory by 5 wickets and with 14.1 overs remaining.
In the Warwickshire League, Kenilworth recorded a winning draw away at Hampton and Solihull in the Premier Division.
After being put in to bat first, James Nason (22) and Neil Goodman (28) made steady progress for Kenilworth.
Liam Newton (29) and a 36 from number eight Guy Pearson all contributed to Kenilworth’s total of 175 all out from 50 overs.
Malakhel with 3 for 21 off 12 overs and Keyte’s 2 for 27 off 12 overs were the pick of Hamptons bowlers.
In reply the hosts lost wickets at regular intervals, with spinner’s Phil Edmonds (3 for 24 off 12 overs) and Jorjeet Singh (2 for 25 off 12 overs) proving useful with the ball.
Both produced a quality spell of slow bowling and were well supported by Joe Boyle (1 for 15), Gregg Peebles (1 for 16) and Neil Goodman (1 for 22).
Only James with 29 offered any sort of resistance for the home team who struggled to 117 for eight from their 50 overs.
In Division Two, Leamington Khalsa suffered their first defeat of the season at the hands of table toppers Lyndworth.
A damp green saw Khalsa struggle with the bat in tough conditions but a stubborn 48 from Karanjit Sahota and a dogged 40 from in form Aman kalsi bought some stability to proceedings.
The visitors eventually finished on 183 all out after 49 overs and they knew an early wicket was key to salvage the match.
They found some success with Pardeep Sharma trapping Ali for 6 and Afzal for 11 inside 6 overs.
But that was the only success for Khalsa as a solid middle order partnership from former Khalsa player Shafiq (72) and Shakeel (81 not out) made the most of a flat afternoon pitch to reach 184 for 3 to take the win and end Khalsa’s unbeaten start to the season.