Other contenders in Tuesday's primary included former Dallas Mayor Tom Leppert and ESPN Broadcaster Craig James.

CNN: Texas GOP Senate primary heads to runoff

Mr. Dewhurst is still considered the candidate to beat in the runoff, political experts said, because of his ample resources, establishment backing and the fact that he is the likeliest to inherit backers of Tom Leppert, the former Dallas mayor who was running third in the Republican primary, with more than 13% of the vote.

WSJ: Ted Cruz, David Dewhurst Head for a Runoff