After Middlesex had been restricted to 217 for eight from their 40 overs in the Group C fixture, Yorkshire reached 54 without loss in 13 overs in reply before a 26-minute break for rain reduced their Duckworth-Lewis target to 197 off 35 overs.
And when the rain returned, openers Andrew Gale and Adam Lyth had taken the score to 81 in 17.2 overs, Yorkshire winning by the comfortable margin of 17 runs under the D-L system.
Meanwhile, Derbyshire suffered their third consecutive Yorkshire Bank 40 washout at Derby when heavy rain ended the Group B match against Scotland with less than 10 overs bowled.
After Scotland won the toss and put the hosts in, only 9.3 overs were possible before a downpour halted play with the Falcons 36 for the loss of openers Chesney Hughes and Wes Durston.
The umpires waited until just before 8pm, but with no sign of any improvement in the weather and with rain still falling, they had no option but to call the game off.
The consolation for Scotland was that it was their first point in the competition after seven defeats, but it was another night of frustration for the home side under the County Ground floodlights.
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