Sharp and Dahm will take office mid-November.
In Norman, voters selected Rob Standridge to advance to the general election in November to face Democrat Claudia Griffith.
Standridge said he has been campaigning since the senator currently in office — Jonathan Nichols — filed for a judge position in 2010.
“It's been over two years,” Standridge said. “I can't imagine a longer campaign and my opponents, to their credit, they've been running a hard race.”
Standridge, 45, is a self-employed pharmacist from Norman.
In south-central Oklahoma, Corey Brooks, 33, defeated Peggy Davenport to face Democrat Mike Fullerton in the general election.
Senate District 43 represents McClain County and parts of Grady, Garvin and Stephens counties. The incumbent Greg Childers was unable to seek re-election because he no longer lived in the redrawn district lines.
“We're certainly very excited and very grateful to those who have supported us,” said Brooks, who is a retired naval officer who spent several years in Washington, D.C., working at the Pentagon. “It seems we've got a pretty good strategy going and that's meeting voters where they are.”
Brooks said he thinks his district is responding well to his Christian conservatism.
All of the races in Tuesday's runoff attracted four Republican candidates in part because no incumbent was seeking re-election, but also because the district lines were considerably redrawn.