Moore won the Democratic nomination over W. Grant Huskey by a vote of 11,642 to 6,076 in their northeastern Oklahoma district. Moore will face Republican Brian Kuester in the general election.
In the race in Creek and Okfuskee counties, Cook defeated Doug Merritt 3,007 to 2,447 to win re-election. Both candidates are Republicans and no Democrat entered the race.
There were two Oklahoma district attorney primary races Tuesday in which no incumbent was involved.
Farley Ward, currently an assistant district attorney in Muskogee County, defeated two other candidates to win the district attorney's race in Haskell and Pittsburg Counties.
Ward received 4,748 votes, compared to 2,899 for Terry Harrison and 1,139 for Russell Tacheira. Harrison is a state representative who decided to run for district attorney rather than seeking a fifth term and Tacheira is currently an assistant district attorney for Haskell and Pittsburg counties.
The position became open when District Attorney Jim Bob Miller was prohibited from running for election in 2010 as part of a deferred prosecution agreement with state Attorney General Drew Edmondson.
Elsewhere, Janice Steidley defeated Patrick Abitbol in the Democratic primary race to replace retiring District Attorney Gene Haynes in Craig, Mayes and Rogers counties.
With 76 of 77 precincts counted, Steidley was leading Abitbol by a vote total of 6,989 to 3,824. Steidley has been drug court coordinator for Mayes and Craig counties since 2003, while Abitbol is an assistant district attorney.
Steidley will face Republican M. Bryce Lair in the general election.