The Tea Party movement scored another victory on Tuesday, helping to propel a dissident Republican, Christine O’Donnell, to an upset win over Representative Michael N. Castle in the race for the United States Senate nomination in Delaware. Mr. Castle, a moderate who served two terms as governor and had been reliably winning elections for the last four decades, became the latest establishment Republican casualty. Republican leaders, who had actively opposed Ms. O’Donnell, said the outcome complicated the party’s chances of winning control of the Senate. With all precincts reporting, Ms. O’Donnell won 53 percent of the vote to Mr. Castle’s 47 percent. The primary drew 57,000 voters, a small slice of the overall electorate. Ms. O’Donnell, a former abstinence counselor who had failed in previous attempts to win office in Delaware, won the endorsement of Sarah Palin, Senator Jim DeMint of South Carolina and other leaders of the party’s conservative wing. “A lot of people said we can’t win the general election; yes we can!” Ms. O’Donnell said. “It will be hard work, but we can win if those same people who fought against me work just as hard for me.” The results on the last big night of primaries highlighted the extent to which the Tea Party movement has upended the Republican Party and underscored the volatility of the electorate seven weeks from Election Day. In New Hampshire, another candidate with strong backing from grass-roots conservatives, Ovide Lamontagne, was narrowly behind his main opponent, Kelly Ayotte, in the Republican primary for Senate Wednesday morning.