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Rutherford scored 108 as his side thrashed Lancashire by 125 runs in the Royal London One-Day Cup opener on Wednesday (local time).
Worcestershire posted 367 at Emirates Old Trafford.
The total was the County's second highest in 50-over cricket against first-class opposition.
Rutherford reached three figures against Lancashire with a six off Australian Glenn Maxwell.
Last week, he scored 123 in a first-class game against Leicester.
The only other Worcestershire player to complete a first-class and list A hundred double on debut was Australian Phil Jaques in 2006.