Yorkshire came back into the contest early in the second period when Dan Hyde crossed for a try, but with their kicker Robin Kitching missing the conversion and two penalties, Warwickshire maintained their lead.
No 8 Max Lewis went over for a try in the 79th minute for Yorkshire to ensure a nervy last few minutes for Warwickshire, but they held on for the victory.
The side face Cheshire in their final group game at the Butts Park Arena on Saturday. Victory could see them top the group and qualify for the final of the Bill Beaumont Cup if Yorkshire beat Lancashire but a big enough margin.
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