Carney coasted to victory over David Lamar Williams Jr. and Coons defeated progressive activist and political newcomer Jessica Scarane to advance to November’s general election.
He served two terms as lieutenant governor from 2001 to 2009 but lost the 2008 Democratic gubernatorial primary to Jack Markell.
Six candidates are competing in the Republican gubernatorial primary amid GOP discontent over how Carney has handled the state’s coronavirus response.
In June, state lawmakers approved a bill authorizing universal voting by mail-in primary, general and special elections.
Meanwhile, the state Republican Party has filed a Chancery Court lawsuit asking a judge to declare the new vote-by-mail law unconstitutional and to issue an injunction preventing universal voting by mail in the November general election.