Mr Crist beat the state's agriculture commissioner, Nikki Fried, in the last big election day before November's vote.
Democrats are eager to eclipse rising star Mr DeSantis amid expectations he will run for the White House in 2024.
Voters in New York and Oklahoma also picked candidates on Tuesday.
The midterms will determine control of Congress for the final two years of Democratic President Joe Biden's term.
In New York state, Democrat Pat Ryan defeated Republican Marc Molinaro in a special election for an open US House seat. That race could prove a bellwether for the midterms.
Read More (...)