The battle between two sitting Republicans was brutal in the final weeks of the election as each fought to retain a congressional seat. Each targeted the other with negative advertising in recent weeks.
The two were elected to adjacent districts in 2010 but redistricting made Quayle's more competitive and the son of former Vice President Dan Quayle decided to run in the nearby 6th District.
Schweikert will be highly favored to win the seat in November because the district is heavily Republican.
Democrats Matt Jette and John Williamson are running in their party's primary.
The district includes Scottsdale, Paradise Valley and parts of Phoenix.