WAUKESHA, Wis. — In the final week of his primary campaign, Tommy G. Thompson, the 70-year-old former governor of Wisconsin, performed 50 push-ups for a local newspaper editorial board to prove he was spry enough for the Senate post he is seeking. He has barnstormed the state for months, visiting with voters and raking in high-profile endorsements for a candidacy that, once presumed dominant, had increasingly felt the encroachment of younger challengers for the Republican nomination.

Mr. Thompson’s political muscles appeared strong enough at his election victory gathering here Tuesday night, as he got the nod from his party in a statewide primary race that pitted him against three fellow conservatives and splintered the Tea Party vote.

“People doubted whether or not I had the stamina,” Mr. Thompson said to a packed room of supporters at a hotel here, adding that he has been “shaking hands like I’ve never shaken before.”

The victory makes Mr. Thompson, who was elected governor four times and served as health and human services secretary under President George W. Bush, an outlier among the many Republican establishment candidates across the country who have been defeated by fresher faces in recent years.