WASHINGTON — Veteran Sen. Thad Cochran on Tuesday night defeated Tea Party rival Chris McDaniel in Mississippi's closely watched runoff, demonstrating an instinct for political survival as insurgent conservatives tried to remake Republican Party.

The Mississippi Senate race shared top billing on a busy primary night in which 22-term Rep. Charles Rangel, D-N.Y., was also fighting for his political life.

Cochran, a former chairman of the Senate Appropriations Committee, made a last-minute appeal to black voters and Democrats in his battle against McDaniel, a state senator who forced a second round of voting after the June 3 primary. Cochran wooed Democrats by pointing to his decades of bringing home federal dollars to help his cash-strapped state. The senator performed better in counties with a strong black population in the Mississippi Delta, unofficial returns showed.

McDaniel, also a former talk-radio host, portrayed Cochran as not sufficiently conservative and faulted him for increasing the nation's budget deficit from his perch on the Appropriations Committee. He was backed by Tea Party allies such as the Club for Growth and Senate Conservatives Fund, both eager to defeat GOP incumbents.

The Tea Party groups had stationed poll watchers throughout the state, worried about Cochran's outreach to Democrats in the GOP contest. Cochran is now the heavy favorite to win a seventh term in November against Democrat Travis Childers, a former congressman.

In other key races, Oklahoma voters chose GOP Rep. James Lankford to be their Senate nominee for the seat of retiring Sen. Tom Coburn and Maryland Lt. Gov. Anthony Brown won the Democratic nomination to be governor.

Republican Curt Clawson won a special election in Florida to succeed Trey Radel, who resigned after he was busted for cocaine possession. Colorado voters tapped former congressman Bob Beauprez as the GOP nominee to face Democratic Gov. John Hickenlooper in November.

But the marquee races were in Mississippi and New York, where Rangel was leadingAdriano Espaillat in a rematch of their bitter 2012 race.

Jeri Ausbon, a McDaniel supporter, illustrated the challenge facing Cochran. She voted in the past for Cochran because "we voted for the party, more than for the person."

Now, Ausbon said, she supported McDaniel because he's more conservative. "We want to get back to states' rights," Ausbon said at a McDaniel rally earlier this week. "We want to get back to what this country is founded on."

Maur McKie, a Cochran supporter, said the senator has done a lot for the state — including his work on agriculture, military bases and infrastructure projects. "He can get things done ... I'm at a loss as to why you throw somebody like that aside," McKie said.

Cochran and Rangel are what's known in congressional parlance as "old bulls" — a nickname given to veteran legislators, often committee chairmen, with deep influence in the House and Senate. Several of their "old bull" counterparts — such as Rep. John Dingell, the longest-serving member of Congress — have chosen to retire at the end of this term.

Rangel had to give up the gavel of the House Ways and Means Committee in 2010 as he was investigated for ethics violations. He argued his years of experience in Washington would be of more benefit to New York's 13th congressional District than Espaillat's tenure as a state senator in Albany.

The district is now majority Hispanic because of changing demographics in Harlem, Rangel's political base since he was first elected in 1970, and new precincts in the Bronx that were added after redistricting. Rangel was criticized when he dismissed Espaillat as having only his Dominican heritage to run on. Michael Walrond, a Harlem minister who is close to Al Sharpton, is also running and could take votes away from Rangel.

While Rangel had a 13-point lead in a recent Siena College poll, political analysts warned the outcome would be determined by which candidate can get his supporters to the polls. "I think it should be close and it all depends on the turnout," said Doug Muzzio, a public affairs professor at Baruch College in New York City. "The key is who's been best at campaigning and messaging."

Contributing: Deborah Barfield Berry in Jackson, Miss.