White, the Democratic former Houston mayor, showed up with his wife at a Houston polling place Tuesday morning and spent about five minutes at an electronic voting booth.
Hutchison and her husband appeared about two hours later at a Dallas church.
Polls show White with a comfortable lead over six Democratic challengers. Only one of them, Houston hair care businessman Farouk Shami, has a well-funded campaign to compete with White.
Early voting runs through Feb. 26.