Linda E. McMahon, a former wrestling executive, easily captured Connecticut’s Republican Senate primary on Tuesday night, clinching a second chance to run for a position she failed to win two years ago.

In defeating Christopher Shays, a former United States representative and longtime fixture in moderate politics in the state, Ms. McMahon underscored the power of being an outside candidate, as well as a wealthy one. She outspent her opponent nearly 12 to 1, and flooded the airwaves with advertisements promoting herself as a political maverick who could bring common sense to Washington.

It appeared that Mr. Shays, who held his House seat for two decades before losing his bid to keep it in 2008, was tripped up by the Washington experience and centrist viewpoints that once made him one of the more popular Republicans in a left-leaning state.

Before a roaring crowd in Stamford, Ms. McMahon took the stage hours after her win and told supporters that she would jump-start a stagnant economy. “We need to give all these career politicians in Washington who have agreed to this mess a pink slip!” she said.