The show won in the Outstanding Short Form Comedy or Drama Series category, whilst the two leads both won in the acting categories.
The awards, which honour "outstanding artistic and technical achievement in television", were presented in Los Angeles. State Of The Union is available in the States through streaming service SundanceTV.
The show wasn't originally in the shortlist, but was added when Better Call Saul spin-off Madrigal Electromotive Security Training turned out to have episodes too short to meet the awards' rules.
Other British-based comedy series to triumph in the awards included Fleabag, the BBC Three series published in the USA on Amazon Prime: editor Gary Dollner and casting director Olivia Scott-Webb picked up prizes.
The dramas Game Of Thrones and Chernobyl were the big winners on the second night of the Creative Arts Emmys. Meanwhile the Primetime Emmys will be announced on Sunday night. Full results can be found at emmys.com
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