The Bears made the most of the good weather to make 313-5 in their fifty overs with Jon Trott making 107 not out whilst Tim Ambrose smashed 135 off 82 ball.
Durham were 77-3 when the rain, which fell in Coventry around 4.15pm,stopped play.
The scorers looked up the Duckworth/Lewis sheets and awarded Warwickshire the win by 39 runs.
Both sides are in next week's Semi-Finals with Warwickshire travelling to Hampshire whilst Durham are at home to Essex.