Alexander had 329,929 votes to 269,8883 for state Sen. Joe Carr, according to unofficial results from the Tennessee Department of State. George Shea Flinn won 34,568 votes in Thursday's primary and Christian Agnew 11,214, while two other candidates had less than 10,000 votes each.
The Tea Party had an early victory in June when Rep. Eric Cantor, the House majority leader, lost to Dave Brat, an economics professor at Randolph-Macon College. Since then, however, a number of incumbent senators have survived primaries.
Alexander, who served as Tennessee's governor for two terms, is expected to win a third term in November.
"Alexander is just not a polarizing figure," John Geer, a professor of political science at Vanderbilt, said. "So I could imagine not only the lion's share of independents going for the senator, but a substantial number of Democrats as well."