WASHINGTON — The Washington establishment delivered a punch to the gut of the tea party movement Tuesday as Mississippi Republican Sen. Thad Cochran, a conservative with more than 40 years congressional experience, narrowly turned back a challenge from state Sen. Chris McDaniel.

Unsuccessful in earlier Republican primaries in Kentucky, Georgia and North Carolina, outside conservative organizations and tea party groups had invested millions in hopes of knocking out Cochran, a six-term senator.

In another setback for the tea party, two-term Rep. James Lankford of Oklahoma won the GOP nomination in the race to succeed Sen. Tom Coburn, who is stepping down with two years left in his term. In the solidly Republican state, Lankford is all but assured of becoming the next senator. Part of the House GOP leadership, Lankford defeated T.W. Shannon, a member of the Chickasaw Nation and the state’s first black House speaker, who was backed by former vice presidential candidate Sarah Palin and Texas Sen. Ted Cruz.

The Republican establishment blames the tea party movement and outside groups for costing it Senate seats — and majority control — in 2010 and 2012.