FORT WORTH — At the opening ceremony of the Texas Republican Party’s convention here — typically a time for delegates to show unity for their party and principles — thousands of conservatives cheered and rose from their seats as Gov. Rick Perry took the stage on Thursday. But a few minutes into his speech at a downtown arena, many in the crowd nearly drowned him out with boos.

The reaction had nothing to do with the governor’s role as a former presidential candidate, but everything to do with his support for a fellow Republican, Lt. Gov. David Dewhurst, who is locked in a fierce race with a former Texas solicitor general, Ted Cruz, to determine the Republican nominee for the state’s open United States Senate seat.

“We need more strong conservatives in Texas, and we need more conservative Texans in Washington, D.C., including my friend David Dewhurst,” Mr. Perry said, ignoring the boos that erupted when he uttered Mr. Dewhurst’s name.

The race to succeed Senator Kay Bailey Hutchison, who is retiring, has transformed Republican politics in the state, pitting Tea Party-backed activists against the Texas power structure, which is led by longtime incumbents like Mr. Perry and Mr. Dewhurst, both of whom have taken stands that have riled grass-roots Republicans and opened them to criticism that they have not been conservative enough on some issues.