HOUSTON — It may be the armadillo days of summer in Texas, but a runoff vote on Tuesday for the Republican Senate nomination has jolted the party establishment here and around the country as a magnetic Tea Party conservative with no elective experience gains momentum against the chosen candidate of Gov. Rick Perry.

Only a few months ago the longtime lieutenant governor, David Dewhurst, 66, seemed all but certain to win the nomination, which in Republican-dominated Texas is tantamount to winning the seat being vacated in November by Senator Kay Bailey Hutchison.

A successful businessman with Romney-esque wealth, Mr. Dewhurst has been allied with Mr. Perry — himself a favorite of the Tea Party and religious conservatives — as Texas burnished its reputation as a low-tax, small-government state with rare growth in jobs. Beyond Mr. Perry, who calls him “a great conservative leader,” Mr. Dewhurst has been endorsed by many party leaders, big business groups and the farm bureau.

But Mr. Dewhurst won only 45 percent of the votes in the May primary, forcing him into a runoff against the No. 2 finisher, Ted Cruz, a Harvard-educated lawyer and former state solicitor general who trailed him by 11 points.